Given how good the new DP cards are, you'd probably buy them even if you could use Base Set-on.
As for the Eevees, yes, they're all in Majestic Dawn (although you may want to invest in other sets for other cards- Great Encounters has Claydol, one of the best, if not the best, cards for hand refreshment, and currently one of the more sought after cards in the format. Mysterious Treasures and Secret Wonders both have a number of great Supporters such as Bebe's Search and Roseanne's Research, as well as a bunch of great Pokemon. Legends Awakened is just awesome all around. The original DP is only good for Dusknoir and Magnezone, though, so don't bother with it.). Leafeon is an excellent card, and one of the better decks in the format, so it's a good choice if you want to get back into the game.