Look around for an old Fender Princeton. Low watts, big sound. Then- consider building a "monster in a box". I started with a heavy plywood shipping crate. I got it for $5 on ebay, and then paid $35 to ship a shipping crate (life sucks sometimes). I lined the inside with 2 layers of heavy carpet remnants and a layer of Auralex foam I had lying around. Then I used a couple of spade bits, drilled three holes in it. Using cable clamps, I hard wired it with one power cord, one short mic cable, and one short 1/4"TS speaker cable, then attached a female to female adaptor to the end of the 1/4" cable. That way you have power for the amp, a mic cable, and a 1/4" cable for an extension cab. I mounted some hinges to the lid, and a couple of heavy duty hasps to keep it shut tight. The shipping crate is mounted to a pallette, which reduces bass transmission to the flloor.
I don't live in an apartment, and I can make all the noise I want. I was just trying to increase isolation. It will not make the amp silent by any means, but it will greatly reduce the noise level, and will also reduce mic bleed. Make sure the box is big enough to allow the amp to breathe a little, and make the cable holes enough bigger than the connectors to dissipate heat from tubes, and give enough ventilation to allow the amp to move air. Also allow enough room for a desk stand or kick drum stand and the mic.
Sometimes I use an amp, and sometimes I use the POD plugged into a power amp into a cab. I think you'll find the POD is a whole different animal when you use it to drive a power amp and a cab, and mic the cab up. Sometimes I just jack the POD into a powered studio monitor and mic the monitor up. If you do that in "the box", you're neighbors most likely won't even know you are home..-Richie