the power supply will cost more than a plate subwoofer amp, and the plate amp will outperform. You can get plate subwoofer amps from Parts Express. come with speaker level inputs, low level inputs, auto turn-on, crossover, phase adjustment, etc.
you only want to run a sub? you already have a home audio receiver?
car speakers and subs in a home environment can work if you build the enclosures correct.
car amps in a home environment fail to be worth the effort.
using a car sub in a home will not be any worse on it than a car, and typically a home environment is easier. i see 30+ years of use out of home speakers on a regular basis.
in my garage i have a Pioneer SX203 from the early 90's running a pair of 12's and a pair of car audio coax. been doing that for over 10 years on that receiver.