What kind of amp do I need?

Being 350w rms each you'd want an amp around 700w rms. 600-800w would be a good range.

There is also the issue of impedance. Dual 2 or single 4 ohm voice coils would need ~700w at 2 ohms. Dual 4's would need 1 ohm power.

There are many options that would work well. Just don't trust the dirt cheap brands like boss Pyle etc. They lie about power ratings. Expect to spend ~120-200 for a decent amp.

Pioneer's gm-d8601 comes to mind.

From 50 rms watts up to 350 rms watts per channel at the stability limit or higher will serve you well. The speakers have the ability to work up to 350rms watts, at specified frequencies and that does not mean they NEED to be driven WITH 350 RMS watts. Give them more than that and you risk burning them out. They may handle 1200 watt transients. If that's their steady diet though, don't expect them to last or operate without distorting. At the stereo shop you can audition several different system on display and discuss with the technician how it might work in your car.

Name brand doesn't always matter I had 2 of the same subs and ran them with kicker 1200 watt amp. If your not worried about cash you can go Kicker, Rockford, Alpine, Boss, JL, it doesn't really matter the mix match brand add much as just making sure that your rms and ohms level out with what the subs can handle, it's simple math though