Well, the first thing I bought was a binder. My mom noticed pretty soon after that, so maybe that'll be doubly useful for you, if it makes your mom notice. As far as clothes go, I would buy:
1. Shirts. Easily the most notable difference between men's and women's clothes.
2 & 3. Boxers and jeans. If you get more self-conscious when wearing girls' underwear, it'll be useful to switch to boxers. If that isn't a problem, I'd go with jeans because my hips tend to make me a little dysphoric.
4. STP/Packer. Peeing standing up is one of the most... exciting? things I've done since coming out. I honestly can't saying peeing has ever been more rewarding.
Then I guess buy as is necessary. As for your swimsuit, I'm going to Hawaii this fall and what I was going to do was wear a somewhat loose fitting binder under a rashguard, and swim trunks. Maybe you could do that? I heard binders get nasty in chlorine, though, so you might want to buy another binder around summer and use your old binder in the pool.