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A 1x15 is going to be your most easy thing to find in most places and be a not to big yet gigable object.
Really the deal with bass rigs is you want as much power as you can afford. You want the headroom, the more headroom you have the the more consistent you sound will be, there is nothing more irritating than when it sounds great until you play your lowest note and it farts out.. The lower the note that more headroom you need. Even if you only have the amp on 3 most of the time the power it of the amp and cab is not being wasted. Personally I wouldn't touch a cab under 350w for any type of gig

As for ampeg? or any of the other companies you need to try a few. And when you do crank the bass control on the amp and play really load so you can ascertain the sound under good amount of abuse. I'm not saying this in a you need to have a bassy sound or you must try to be Sunn O)))) it's about understanding the nature of the instrument... And blowing up a few speakers and amps at "normal" gigging volumes over the years gives you perspective...

For what it's worth..
For the last year I've been using a peavey 1x15 & 2x8 cab, I like it a lot, has tons of headroom
As for a amp I've given up on tube amps and use a (SWR) preamp with a crown power amp

maz91379 wrote:I guess I'm not completely sure how wattage works in solid state amps / what I need to try as far as wattage ratings on cabs. Mostly understand ohm ratings.

Yes. Not to get into the tube vs SS thing cuz I am not an authority..

maz91379 wrote:Like with guitar I'm used to picking speakers rated at wattage or a bit over my guitar amp so I can get a bit of speaker distortion. I guess that's undesirable with bass?

Depends on the person. some bassist like speaker distortion, personally I find most average bass cabs under 400w distort at lower volumes then they should going by their ratings.

maz91379 wrote:Like with a 350 watt amp at 4 ohms , about half at 8...would a cab rated for 350-400w hypothetically be enough or would I want to aim for like 5-6+ ideally? Or does that sort of also depend on construction / speaker/ particular cab etc?

Pretty much, but..

maz91379 wrote:Oh also! What's the deal with program ratings?

program is important with bass speakers because one issue you can have is that over a period of time if and when your speaker heats up it's functionality and efficiency lessens which is perceived as decreased volume, so you will want to turn up louder and louder and eventually.. [we are talking hours here...]

maz91379 wrote:Also also complete tangents. Pretty sure I could find some suggestions if I dug through search but I don't quite remember how this works. What's stopping me from loading higher rated bass or PA speakers into a guitar cab and running it at 8 ohms so I can do both guitar and bass through it? I have a silly overbuilt atlas 2x12 I imagine would work similar to a sealed cab. Would my only downside be zero speaker distortion for my 30w guitar amp? Any potential upsides like more clean loudness ? I currently have a vintage 30 and a green back of some variation in it....

Nothing. I used a cab like that for a few years [it had 2 200w EV 12s @ 4ohms] sadly I blew up one of the speakers but A. I was using a SVT, and B. it was a used homemade deal with no ports or baffling. Sealed cabs can work but, you will want some kind or dampening material inside to help with resonate frequencies getting out of control..