I am pretty sure that my amp doesn't have a crossover built-in, I'm not sure what differences there would be though. It is a 4 channel amp with gain control knobs on it.

If the only controls it has are gain control knobs, then you are correct, it does not have a crossover built in. There would be other controls for crossover, such as high or low pass switches, and perhaps even a knob to set the crossover point.

What kind of crossover should I get.

Actually, you can do a poor-man's crossver by using something like F-mods. Very inexpensive, and they work. I've used them myself from back in the day before I had an amp with built-in crossovers.

But if you've got the money, I'd just dump the amp and buy a proper one that's got crossovers built-in. That gives you the best control, and also is the least likely to induce a ground loop noise problem. Since you're planning on adding a subwoofer anyway, now is the time to just replace the 4-channel amp with a 5-channel amp that's got crossovers built in. That's your best bet.