Subwoofers???

[tubbedII]

I want clean, powerful bass as simply and cheaply as possible.
It all depends on your ear for what "clean" is if you can do it for cheap.

So, will I be able to do this with my 1200 watt Sony Xplod amp?
Hard to say without knowing the details of it, but post up the channels, product number and such and it would be easier. Either way, the amp was free so it's worth a shot

What type of sub should I get and how many? (diameter, wattage, etc.)
I would go with 2 10" subs rated at what ever watts the Sony Xplod puts out at RMS. Any known name brand should give you what you are looking for.

And what type of box should I put it in? Ported/non ported?
Sealed is my preference. Easy to buld and no tuning required. If you plan to build the enclosure yourself (and probably your 1st time since you say you don't know anything about car audio), this is the only route I would go.

All advice is appreciated.
My only advise is to measure the area where the enclosure will go before buying anything to make sure you can build a box with enough air space for the speaker(s) you get.