New amp ?

I'd recommend a small Ampeg practice amp, unless you plan on playing with other musicians. If that's the case, then you'll need a larger combo--preferably one that can drive an extension speaker, or a separate head/cab combo.

 

What's your budget? Do you want a combo or head/cabinet? Do you prefer new or used?

 

Tube vs solid state is a little different than the world of guitar playing. SS is much more widely used by bass players compared to guitar. The trend is heading toward smaller and more lightweight--which means solid state.

 

Check out GK. Great sounding, light weight combos and heads/cabinets. Gallien-Krueger Bass Amplifiers | Musician's Friend

Look at the MB115 or MB210 combo or the MB200 head with an MBE series cabinet.

 

GK all the way, go with the mb200 and a mbe 4 ohm cab, try and wait for a 15% off deal from MF or GC and you should be able to keep it under $500.

 

Drop by your friendly neighborhood music store or pawn shop and pick up a second-hand amp. I think a 1x12, 1x15, or 2x10 combo is plenty for loud basement playing. Personally I am a Peavey guy, I think a used Peavey combo is the best bargain for a beginning player.