Right or wrong, I've been using a mid-level consumer-grade integrated stereo amp since Moses received the Ten Commandments.
I've also been using, get this, Optimus LX-7 speakers. Don't laugh, the mixes turn out great on every other system I've ever tried them on, from friends systems to the raggedy old boom-box and everything in between. I don't know why this combination works as well as it does, I'm just glad it does. Too bad they dico'ed them several years ago. They are the best small consumer-grade speakers for monitoring that I've ever heard.
They are very flat and natural sounding, but more importantly, I know them. Very well. I have never invested in a set of professional studio monitors, though I thought about it many times. I'm not going to waste the money because I don't think I could get my mixes to sound as good on a strange pair of speakers after using the ones I do now for so long.
If you wanted to hook them up to your computer, you could use an amp or you could buy active monitors.
They should be set at ear level, turned in pointing at your mixing position, and they should be an equal distance from each other and your mixing position. Think equalateral triangle.
Ideally they should not be on the floor or in a corner. Nor should they be (usually) within a foot of a wall. Mine unfortunately are up against a wall but angled out because I don't live in a palace and real estate is at a premium. You will have to compensate for any of these conditions by carefully EQ'ing your mix. Again this comes from knowing your monitors.
Another important point is that for whatever your distances are with whatever monitors you use, you have to be far enough away for the bass wave to develop or your mixes will have too much bass responce because you will be compensating for something you haven't heard yet and roll up the bass. The opposite will happen if your speakers are on the floor and/or in a corner. Apparent bass responce increases and you will compensate by rollin the bass off and your mixes will have no bottom end, except on your system.
The distance for my LX-7's is 57" center-to-center between monitors and 57" from my position to each of the monitors at the center of the cabinet.
I have my position marked on the wall and on the floor so my ears are always exactly where they are supposed to be in the mix position. If I am anywhere else in the room while I'm listening to a mix I avoid the temptation to change anything because it sounds different away from my position. This is critical to getting consistent mixes and having them sound good played on different equipment.
I can't recommend a set of monitors as I've never priced any nor have I ever listened to any. I've heard that Tanoy's are great little monitors and JBL also makes good monitors. Mackie makes active monitors as does Alesis.
Hope this helps.