You need a 4 buss mixer. Basically, it is like having 2 mixers in one. This allows you to listen to what you have previously recorded while recording new tracks on top of the old. If you just have a basic stereo mixer, you will be recording old tracks on top of new tracks...very messy. You can get a used Mackie 1202 between 150 and 200. If you can afford the new model, I would go with it.
The 1202 has 4 stereo channels and 4 mono channels so you should have plenty of room to grow. The best thing though is the quality and even if you end up with a large home studio you can always use the 1202 and be happy. If you had more money to spend then I would recommend one of their other units. (This is in reference to AUDIO .wavs which you will be recording at some point and has nothing to do with .mids).
Cheap powered speakers may be ok right now, and you might even be able to use them after you get a nicer amp/speaker setup, but you probably will not like the sound---especially after listening through headphones. You cannot mix a song using headphones (you need MONITOR speakers).
The EQ will be all wrong and it will not sound the same when played through a home stereo or car stereo (just something to be aware of).
As mentioned earlier, you can blow your home stereo equipment if you play your synths through them.