Make sure to check your local craigslist adverts. If you are near any city of any size, you can find plenty for midi entry. Many Casios will work for this. Not slim pickings at all in your $100-$200 range actually.

Don't worry about latency - your'e just entering midi data. Play back the midi data via an internal synth in the computer. That's where the latency issue hits, not with midi data entry.

You can even pick up a USB/Midi keyboard in that range. I bought an M-Audio Oxygen 49 for just over $100 at audiomidi.com

But you might want to take Pat's advice and get a used Casio or Yamaha that has a GM sound set built in, and buy a UNO usb-midi adapter to go along with it.