Magic may definitely seem intimidating. It's got a rulebook over 200 pages long, and passed 10,000 unique cards back in 2008. I'm sure you've heard stories of people spending tons of money on magic collections. But, done right, Magic can be quite approachable and quite affordable. Whether or not this is "easy" depends on your goals. If you just want to play magic with friends and have fun, then this can be done quite easily. If you want to win tournaments, this will take a lot work. There is a whole spectrum in between.
Learning to Play
If you have a friend or friends who play Magic, odds are they will be very happy to
induct you into the cult teach you how to play. Having friends who already play or want to learn with you is also really important because having a dedicated play group will make learning a much more pleasant process. If you don't have such a group, see if your local game store has casual events so that you can find one. Learning to play against strangers is a much less forgiving experience.
There are potentially a surprising number of people in your life who already do or once have played Magic (especially if you already have friends that play other CCGs). Try leaving a few decks of Magic cards on your desk and see how many people go, "Oh, you play Magic too?"
If you don't have friends who already know how to play, you can read the Magic basic rules, which are only 18 pages. These describe the bulk of the mechanics you need to understand to play (although somewhat comically omits the most important 2 pieces of information: you start with 20 life and lose when you hit 0).
Duels of the Planeswalkers is also a decent tutorial in computer game form if you prefer that medium, although it can get a bit slow due to the game waiting to see if you want to do something every time you could do something (which is quite often in Magic). Magic: The Gathering Arena is another digital option for leaning to play.
My personal belief is that Magic is best played in-person. It wasn't designed or optimized to be a digital experience. A digital version of Magic can be a good way to learn and can let you play when your playgroup is not around, but if you have physical decks and a playgroup that you can get together, you should do so.
The Card Pool
While the card pool seems the most intimidating aspect of the game, it's a bit of a red herring. When playing a game, you only care about the cards you and your opponent are using. A normal deck is 60 cards. Typically over a third of a deck is going to be lands, which don't vary that much. That means that in a normal game of magic (i.e. not Commander), there are fewer than 100 distinct cards you need to think about, which is less than 1% of the card pool.
Even when you start building your own deck, you will be limited to your collection which, at first, will probably be much smaller than 10,000 cards, and probably under 1,000 distinct cards. Only when you want to expand your collection or build a competitive deck do you start to care about all cards in Magic, but even then, not necessarily. If you want to expand your collection, start with a search tool (such as scryfall.com) and look for cards you want, or a site where people post decklists that you can use as a starting point to look for particularly exciting cards. Meanwhile, if you want to get into the tournament scene, you can (and should) start with a tournament format with a limited card pool or one that doesn't require you to have a massive collection; more on that later.
Building a Collection
If you have a group of friends that already know how to play, odds are one of them will have decks that you can borrow when you are starting. Just make sure to tell them you want to borrow an aggro deck, as using a combo or control deck is terrible when learning to play (If no one in your playgroup has any aggro decks on-hand, try finding a different play group :P).
Alternatively, if you have a group of friends that are learning Magic together, consider either making some bulk purchases together that you will split among the group, or having one person buy cards that everyone will use at first (until people have built out individual collections).
If you want to start playing without needing to build a collection, buy some preconstructed decks. Wizards prints these pretty frequently, and they can give you a great starting point in terms of having a deck that works, so you can start playing right away, then step up to tweaking the deck, and then eventually try to build one from scratch. Check out the Ravnica Guild Kits as a good example. These are especially good if you have a group of players all learning Magic together.
If the deck building is what excites you most about magic, you should get a Deck Builders Toolkit (from any recent set) and/or look online for someone selling a bunch of cards for cheap. You can often get a bunch of cards in bulk for around 1-2 cents a card on the secondary market; these aren't going to be the best cards or tournament staples, but they will be a bunch of cards that you can start building decks with.
Building a Deck
Building a deck is a skill unto itself. There is a lot of advice on how to actually do it. I'm not going to try to tackle that here. This is just a few pieces of advice on how to approach deck building (rather than on how to do it).
If you have friends who are established players, ask them what they take into consideration when building a deck. Tell them what you want a deck to do (after you've played a few games) and have them help you build it. Otherwise, start with a preconstructed deck.
Once you have your own deck, play it and tweak it after every few games. Take out cards you don't like, or cards that keep feeling weak, or cards you keep not being able to afford (mana-wise). Put in cards that are exciting, or cards that do things you keep being frustrated at not being able to do, or cards that have a better mana cost, or cards your opponents used to trounce you.
Once you've tweaked a deck for a while, make another one. Then tweak that one. Do this enough times and you'll get a sense for how to build a deck. And, better yet, you'll get a sense for how to build the type of deck you like to play.
The most beginner friendly "format" (and the one I use when teaching people how to play Magic) is regular 1-on-1 60-card Magic, but where your deck (you being the beginner) is much better than your opponent's deck. This gives you plenty of room to make mistakes and still possibly come out on top. If you have a friend who is both an experienced player and a good sport, go for this.
Alternatively, if no one in your playgroup knows how to play very well, this is usually sufficient beginner-friendliness that format doesn't matter. No one has vast expertise to throw around. Just make sure no one has spent wildly more money buying cards and this should shake out pretty well.
If you are joining an experienced playgroup with competitive people, try for multiplayer (either free-for-all or something exciting like Star Power). My first ever game of Magic was against two very experienced friends, yet I still won because they spent the whole game fighting each other (because I had no idea what I was doing), and then I was able to finish them both off. Two-headed giant is also a great format possibility as you have an ally that can give you unbiased tactical advice and help you with rules questions without giving away too much information to your opponents.
I'd stay away from Commander at first. It is a very fun format, is multiplayer, and is often more about doing interesting things than it is about winning. I highly recommend it... once you know what you're doing. However, as a new player, there are a lot of pitfalls: there are a lot more cards you will have to care about in a commander game (due to the restriction that you have only one of each card in a deck), the complexity of the game state tends to get much higher than that of a normal magic game, and Commander games tend to run much longer than normal games, making mistakes more expensive.
Tournaments are a totally optional part of Magic. I have friends who have played Magic for years and never played in a tournament. But they are also an option if that's what excites you.
Magic has 3 general types of tournaments: Sealed, Constructed, and Draft. Sealed is a tournament where you open a set of cards at the tournament, build a deck out of them (plus basic lands), and then play with that deck. Draft is similar, except that it has a complex process for how you select the cards you keep. Constructed is where you bring a deck you have made and play against other people who have done the same.
If you are a new player who wants to get into tournaments, I recommend sealed tournaments. These are much more affordable price-wise (all it costs is the admission price; you don't have to spend hundreds or thousands of dollars on a deck), you often get to keep the cards you open (thus growing your collection), and the games themselves tend to be a little more straight forward (it's more about cards that stand on their own merit rather than complex card interactions or decks tuned to the metagame).
While all of these things describe both sealed and draft, draft adds the added complexity of the card selection process, which is yet another skill to learn (worth doing eventually, but not needed at first). In sealed, it's just rudimentary deck building and playing magic. Set releases or prereleases are especially good for new players because at that point, people haven't had as much chance to use the cards in that set, thus reducing the experience bias even more.
If you want to get into constructed, there are a bunch of formats within that genre (Standard, Modern, Legacy, and Vintage being the big 4). You should probably start with Standard, in which only cards from the most recent few sets are legal, thus reducing the number of cards you will need to learn to be competitive in the tournament format.
I'd recommend playing for at least a few months before joining a tournament. You need to be at least moderately proficient in the rules before you play in one (regardless of format) because your opponent will almost never let you take back a mistake in tournament play. Additionally, you need to either have some practice in deck building (especially for sealed or draft) or have copied a competitive decklist (if you're playing constructed and don't want to design your own tournament-grade deck).