I've played MTG casually a couple times, built some starter decks, but gave all my cards away in a purge a couple years ago. I want to get back into Magic, but after reading about all of the upcoming changes at the end of this summer (so, a month from now?), I'm not sure how to pick it back up. Should I buy a core set anyways to start building decks, or hold off?
If you want to start with a core set, Magic Origins is fine to buy - it's going to be in standard another 18 months. The changes are all in the future: no more core sets after this one, two-set blocks, changed rotation schedule. But that doesn't change that Magic Origins is here now!
Even if nothing were changing, it'd still be another year until the next core set, and if you're going to actually get into the game, a year is plenty of time that by then you wouldn't be worrying about core set vs "expert" expansion anyway. So it doesn't seem like the changes are really taking any intro-level stuff away from you. Besides, Wizards knows they need to keep the game at least a bit accessible to new players; I'm sure they'll keep creating things like the Duel Decks that'll give you a way to pick it up even once the core sets are gone.
You can also get Clash packs, which are really good value for their cost. The new release "Outlast" is said to be worth Twice its price. they give you two Set Decks of 60 cards that work Flawlessly. I have bought this pack myself so I know from experience. Alternatively there maybe certain places you can go that Host "Friday Night Magic" it is getting increasingly popular, that's how I started up again recently.
There are Deck builders toolkits available that give you a lot of cards like over 300. with every colour, from them you can make decks that suit you. the hardest thing I thought to get used to was the introduction of multicolour decks but they are easy to pick up.
Just make sure you stick to 60 cards as a precaution as in my opinion it makes it easier to get what you need out of the deck. Also Check the website: magic.wizards.com that should have a place to show you the rules and how to play. Good Luck!