Stupid question - In a four piece band, what am I looking for for my vocalist.

Do I need a mixer and beefy monitors for my vocalist to be heard over the drums.

Got a space that's the size of a large master bedroom

Drums, bass, guitar, guitar, vocals.

Not really looking to record, just something that can ampliy vocals.....(cheaper is better)
How about all of you going in the box instead?
You can lower your volumes and at the same time get better practice in this small room, otherwise you'd probably piss the neighbors and get yourself deaf in the process.

You can go with one of the many available headphone practice mix solutions, like this for example:

IF you want to go traditional route and get your singer loud enough, you'd probably be best off to find a powered mixer with effects and buy PA wedge monitor/s, in other words a PA system. Maybe just one powered speaker will do, but they usually don't have effects in case you need vocal effects.

Something like this: