I was more into it for hunting so I got a .303 first. My second gun was a mini14 in .223 (I very much loathe that rifle), then I got a 10/22 and it instantly became my favourite. Then a browning X-bolt in 308, Remington 870, AND then the safes got bigger, and my bank account got smaller... starting collecting milsups, shooting pistols, so on, so on.
Since target practice is your purpose, I'd get some sort of 22LR bolt gun, 10/22 is great but for me, more then not I just spent time dumping ammo through it with little concern for my groups (And many others have done the same). A bolt gun will naturally slow you down, so you focus more on your fundamentals. As for a second gun, it really just depends what on what you're into. I kept my collection small for the first few years, mastered the few rifles I had. I would advise you to do the same. I have too many friends that are "collectors" and own dozens of guns but still cant shoot for s**t. Collecting guns is like a drug addition, its hard to resist the temptation, especially with all the great deals you can find on the Equipment Exchange.