Best box for Alpine Type R?

I always reccomend between 300-500 rms for that sub in the sealed enclosure.  As for an amp, the mrv-t420 would push it, but probably suck more juice than you want to supply.  The lowest impedance an alpine amp can run is 2 ohm, and thats only the mono sub amps.

Look into a JL amp the 500/1 would be my reccomendation, it puts out 500 rms between 1.5-4 ohm.  Its the best amp in my opinion for flexability.  in the future you can get a 2 ohm sub and it will still put out 500 rms.

There are also some 1 ohm stable amps out there, but im not familiar with any of them, i'll let others chim in here: