Defer this decision until you know where you're going to play.
I'm going to assume you have an acoustic drumkit, which you won't be mic'ing up. So the drums set a baseline volume which the other instruments and voices need to match.
You actually don't need much to achieve this. The guitarist just needs a modest amp - one step up from a practice amp, something like the Roland Cube (not the MicroCube). The bassist needs something a bit bigger, because bass needs to shift a lot of air.
I'd suggest that the keyboard also be plugged into a cabinet. It could be a similar size/power to the guitar amp, unless your keyboard is expected to provide bass elements, in which case it will need to be larger and more powerful. But do make sure it's a keyboard/PA amp, designed to cleanly amplify without adding distortion or tone.
That just leaves microphones. It's possible your first venue will have its own PA, in which case, use it. Even if it doesn't, your second might - so hire (rent) a PA instead of buying one at that stage. You don't need much - a mixer with as many inputs as there are voices, and another small PA amp/cabinet.
At this level, monitors are a bit of a luxury, but you'll be grateful for them. So if they're on offer, take them. You might be able to improvise monitors by using the practice amps you use at home.
If and when you move on to bigger venues, it becomes all the more reasonable to expect the venue to have its own PA. I would resist the urge to buy instrument amps that will fill large venues. Play at the volume you practice at; point mics at your on-stage cabinets and have the house PA amplify them at the audience. It should be quieter on stage than in the crowd. DI where it makes sense.
Some acts fill the stage with huge cabinets. Some of them are actually using them. Lots of them, however, are just for show -- the real sound is from a small mic'd up cabinet. Seasick Steve plays festival main stages with a MicroCube.
It may be that you find yourself on a circuit in which you frequently play larger venues that don't have their own PA. Only when that turns out to be the case, should you consider buying your own PA -- by which time you will have picked up enough experience with hired equipment and house equipment that you'll know what you want.