To address the initial post, I think the smart decision would be a bass rig.
My opinion, based on some experience in years past with gigging, and all of my experience as a whole in rehearsal spaces, studios (well, A studio), basements and garages with other musicans:
The guitar rig is fine IF this is true:
NOT a metal or hard rock band
Respectful and experienced group of musicians
Volume is kept to only the level that some louder acoustic instruments could be used without amplification, i.e. horns, hand drums piano, etc
IF any of those things are false, then the smarter solution is a bass rig. I think B string nailed the analogies pretty well. The fact is that our ears are "calibrated" for the human voice. We hear a certain part of the audio spectrum more easily than the rest of it. This part of the range we hear better in shares the frequency spectrum with the standard range of guitars. The range that bass guitars live in uses quite a bit of it, especially the upper strings on a low E 6- string. The lower notes, dip down to near frequencies we can't even hear, so they kind of just muddle together. The ear needs the other part of the spectrum that we can hear to help us out... thankfully there are also harmonics that are higher present in each note. We need help discerning the lower notes from nondescript rumble. This requires a lot of moving air. More cone area moves more air. The frequencies we need to vibrate the air at need cones that can move in and out quite far. It takes lots of power to make the cones produce these frequencies at high enough air pressure to be useful in a group of other instruments. Guitar rigs in the majority of these situations just can't meet either the power or air pressure requirements that playing a bass guitar needs. Guitars don't need to be as loud for us to hear them, the amps have less output. The speakers don't need to move as much, or handle as much power, so they simply aren't designed for use in a portion of the bass guitar's range at much more than unusable levels. You can cut your lawn with a string trimmer, but a mower is actually designed to do that. It's a BASS guitar, not a bass GUITAR. Yes they have the same shape, use strings, and have the same notes an octave apart. But they are very different instruments, and need at the least, different speakers.
The suggestion for a 200-300 watt 115 combo is valid and a sturdy minimum that can be had for anywhere from under $100 used to near the budget you mentioned.
Now, let's talk about that budget... if you really are willing to get a rig truly worthy of being a good equivalent bass rig to a 50 watt Marshall all-tube half stack, that budget is pretty darn near what you'll need shopping new. The equivalent brand in the bass world is (arguably) Ampeg. There are many many other brands just as wonderful, been around for decades, great customer service, yadda yadda, but in the bass world, Marshall isn't one of the top dogs. They actually dropped out a few years ago. They have some good bass amps, but the cabinets.... for the price, meh.
