I am thinking of buying an amp; Suggestions?

TNBXIII

Hello Guys,
Sorry to bother you guys once again with my newbie questions.

As you all know by know I am going to upgrade my car audio system. I already bought the speakers and head unit, but I think an amp would be a great addition if I am going to do a full audio install.

Here are my specs:
Pioneer FH-X830BHS
RMS Power Output 14 watts
Peak Output 50 watts
RMS Power Bandwidth 20-20kHz
Preamp Outputs 6-channel
Sub Preamp Outputs Yes

Alpine SPR-50C
Sensitivity 87 dB
Frequency Response 70 - 29k Hz
RMS Power Range (Watts) 8-100
Peak Power Handling (Watts) 300
Impedance (Ohms) 4

What do you guys think would a be a great amp to power this speakers?
Also if would be great if you could suggest something that could fit under the seat, or somewhere where it does not take too much space and has no risk of heating up.

Thank you guys, and sorry for all the trouble.