This is difficult. A lot of things can be done on good headphones, but some things I find very difficult. One example is setting reverb levels, but as the say YMMV.
Mixing and mastering sets rather high demands on speakers. The basic idea is that in the studio the speakers should show the mix in all of its ugly truth. In order for you to fix it. They are used as tools.
But many consumer speakers are made to make the sound as pleasing as possible. By hiding a lot of that important information you want to hear in order to make a good mix or mastering. Hear the purpose is to please.
One typical situation is where the speaker uses a small ported (or vented) cabinet tuned typically to between 80 and 160 Hz. The port will enhance these frequencys a to make your ears believe they hear low bass frequencys, making the sound more pleasing. But the side effect is that most or all other bass frequencys disappears. It is very difficutl to mix a typical "sub sonic" bass drum on these speakers, say from a Roland 808, as a lot of the sound simply is not reproduced by the speakers. And yes, the Bose Companion 2 is a typical example of that kind of design.
You can learn to mix and master on this kind of speakers. I do not recommend it though. And once you move to revealing speakers you will never want to go back.
My suggestion, given your limited budget, is instead that you search for used hifi speakers and an old stereo amplifier. It will take more place and possibly look ugly but it would give much better support when you mix and master than a typical PC addition. The amplifier makes very little difference as long as it has an adequate power output, say 20W or more. You will need cables fitting the amplifier on one end and the PC on the other. These should be easy to find in Radio Shack or similar places. As for hifi speakers, my ideal for mixing and mastering clearly is closed boxes (no bass port or venting), but those are quite unusual. You should be able to find som larger (size matters here), older, ugly, speakers in second hand places at low cost. Just check that all the speaker elements are still working (feed them noise and listen to each element separately). This will give you a much more revealing speaker and will allow you to polish your own mixes better than on PC speakers. They will of course work on commercial material as well.
Anyway, my 5 cents.
// Gunnar
