My bass player is looking to pick up a combo for our band's acoustic gigs, jams, and for kicking around the house. It has to have… good tone?
He's looking to spend on tone, so don't let budget cloud the suggestions.
Well in the bass world class D power amps have taken over so most of the amps coming out weight less than 6 lbs, so limiting yourself to just a combo isn't necessary. I would tell him to try out a ton of stuff since most different bass companies amps are voiced to their own "sound".
Stuff I would recommend to check out:
Mesa Walkabout and the new Lunchbox heads (Prodigy & Strategy)
Gallien Krueger MBs
TC Electronics RH series (BH series are great for budget and worth it as a practice amp)
Genz Benz Streamliner
MarkBass (Only if he never wants any grit or dirt )
The bass pedal world is insane so you could buy just a Class D power amp and run it with any pedal or you can use them with any of the amps. Someone is always building the latest and great amp-in-a-pedal Biggest thing I would say to be careful with amp selection is to not get a modern Ampeg microhead since when I was looking into them they were having HIGH failure rates. Better option for Ampeg tone is just to get a Tech 21 VT Bass.
Also since you said price isn't a factor I would suggest into looking into AudioKinesis' cabs or maybe a fEarful design. Josh has a AudioKinesis if you want to talk to him more about it. These style of cabs are awesome because with the proper speakers the design of the cabs really push a lot of air out and at really light weights due to specfic building material choices and neodymium speakers.