im using a using an Ibanez IBZ10B with a Squire CV jazz bass.
I have one of those in my office. It's frankly pretty bad, gets all buzzy playing anything lower than the 5th fret on the E string. This is not really all that surprising, though, given what it is. I kind of wonder if the cheapo 10w Peavey is any better, but it has the same kind of limitations so while it might be a little better, probably not enough to matter.
Anyway, there are two issues here: power and driver size. In principle, you don't really need a ton of wattage to sound OK, but a single 6.5" driver is just not going to get it done unless it's a really really good driver, and that's not what you're going to get in a cheap combo amp.
Even just for home practice, look for something with at least 40w and at least a 10" driver.
The good news is you can get there for $200. As has been noted, this is Fender Rumble40 or Ampeg BA-110 or Hartke HD-50 territory. Any one of those will be just
miles better than the little Ibanez. Seriously, it'll be like night and day.
Definitely do the upgrade. I know that's what everyone always says on TB, but trust me, this time we're really not kidding. The Ibanez is garbage, all of these other options are not.
If you're going to be moving it around much, get the Fender—it's under 20 lbs, with the other two are in the mid-30s. If not, I'd probably get the Ampeg. Little bit cheaper, and it's cut so you can do a wedge-like placement, which will be better when you're standing.