Hi-fi speakers can go loud, but you're getting quality rather than out and out volume with them most of the time. Saying that, even the most modest bookshelf speakers that I've owned (mission m72) were plenty loud enough.
If you want music, then definitely get a stereo amp and speakers. You can hook it up by using a headphone jack to 2 x phono converter cable, easily purchased from any high street electrical store or from the interweb.
As far as what speakers and amp to get, definitely only look at stereo solutions, as surround sound will eat up your budget if you're looking at separates. There's always the floorstanders vs bookshelf debate, which does depend on your budget and the size of your room. Are you looking into the second hand market? You can get some serious bargains and really increase the quality of gear that you can get. I would have paid double the price for my system (if not more) if I had bought everything new, but the sound quality certainly hasn't decreased over that time noticeably, and it definitely hasn't degraded by half.
In summary, yes you can connect your hi-fi to your computer. Have you got a sound card? This does make a difference, and after some new memory it's definitely on my list of upgrades. My CD player is much better anyway for serious listening, but it would eliminate a lot of needless electrical interference which is very noticeable.
