What do I need to consider when buying amp and sub

Velodyne subs have the high level speaker input. Run 2 sets of speaker wire from your amp. One to your mains and one set to the left and right speaker inputs on sub. It is high level so it isnt gonna pull power, just obtain the signal. You can still use the sub Xover to blend into your system.
I use the vel with Focal 918s and set it just enough to add punch on the low end. works nice . Hope this helps.

I am pretty sure that I am going to get a JL Audio sub. What should I be looking for on an amplifier?

If you are going JL, you'll need an integrated amp with either pre/line level-outs or tape out.

Jeffatus - if your dealer sells the JL's then they will have all the answers. I myself went from RELs to a JL and it was the best move I've made regarding a sub. The JLs are best used via the XLR connection over the RCA connection and the better the cable the better the sound. I've tried 3 different XLR cables and finally settled on a Purist Provectus (dealer disclaimer) for the best results. The problem was the cable was as expensive as the sub! And don't forget you'll require decent power cord as well . Yes it's madness but in the end worth it.

If your main speakers have ports then most likely the best intergration will be achieved if your sub is ported