Based on your listening preferences I would go with the 10" sub to save space over the 12" sub. I looked up some prices on
www.Crutchfield.com and this is what you're working with so far:
Infinity Reference 6800cs - 179.99
Infinity Perfect 10.1 - 134.99
Q-Logic QLH-CS10 Single 10" Box - 53.99
Total = 368.97
I skimmed through Crutchfield's selection of Amps and none of them stood out as an obvious choice. I am partial to MTX so I would probably choose the MTX Thunder564 ($339) which will send 70 watts to your components and 280 watts to your sub.
The Alpines will give you slightly better SQ but none of them have the power output that would be ideal for the Infinity Perfect. For example, if you went with the Alpine MRV-F340 ($399) you would send 55 watts to your components and only 130 watts to your sub. You pay $60 more for less power, an LCD screen, enhanced noise reduction, subsonic filter (only really needed for ported enclosures) and the Alpine name.
Since you mentioned Kicker in your original post I will mention the Kicker KX-550.3 3-channel amp ($379.99). I don't particularly like Kicker but this amp may suit your needs. It will send 75 watts to your components and 420 watts to your sub from its 3rd channel. Please note that if you choose this amp you will want to purchase the Infinity Perfect 10.1
d dual voice coil model to get a 2ohm total load. I think this amp probably has the best value per dollar for what you want to do.
Now, if you are willing to spend the money, the JL Audio 450/4 is a great choice but I think it is about $700, far more expensive than anything else I mentioned. This amp will obviously sound much better than the MTX, Kicker or Alpine and will give you 75 watts for your components and 300 watts for your sub. There is just no comparing this amp to the others...it is simply better and worth the higher price.