In response to your specific need, there will be very few cards in Magic 2015 that existed in any set since Magic 2014 and even then it'll be a limited overlap. This is simple pragmatism on Wizard's part; if half the cards in the new set are already in even the new players' hands, then people aren't as interested in the set. So if you're looking for cards that don't exist in your collection, you should be fine.
A lot of the "reprints" will actually be from old sets like Mirrodin (for example, Darksteel Citadel is back, and we can expect to see a lot of the old Convoke cards from original Ravnica: City of Guilds), and you will never have seen them before. So you should get a good sample of new blood for your collection.
On the other hand, if you want definite new blood, getting a booster box of Theros or another "Fall set" would be a more reliable way to go.
Hope that helps.
Some Background Detail on Core Sets and new Cards:
Historically, there was a shift in 2009, when the set Magic 2010 was released.
Up to that point, core sets were basically "Standard enablers". Their job was to provide a set of cards to allow players to build basic decks for the main 2-year rotating format, which would then be "powered" by the main mechanics of the "Expert" sets. They also acted as an intro product to the game, but this was fundamentally a secondary role. The main evidence of this focus was the fact that Core Sets didn't provide any new cards, and little to no new art, which meant that they were generally a hodge-podge of cards with no unifying theme, a poor limited environment and (generally) a lower power level.
Magic 2010 changed this by saying "Look, this is the product that lays out what Magic is", not just what it's doing this year. We're going to have the Magic rings, the Necromancers, the wacky Goblin hijinks, the Fireballs, and if a card we want for it doesn't exist, we will make it exist. Note that this is the inverse to the expert set's dictum "If an existing card will fit with our theme, we should put it in".
As Hao shows, this leads to the Core Set having a limited number of new cards. But it's also meant that the reprints they pull in are better chosen, and generally chosen with an eye to new players seeing new cards.
The set is also far more "draftable", which I would argue is the best way of gaining value from your booster packs. I've been regularly drafting newbie 2014 on Magic Online, and it's a blast.