I went down a similar path to eventually starting a full band to accompany me on stage in paying gigs vs playing just for fun. My band has bass, two guitars, drums and vocal mics for all four musicians.
What you would need for amplification of your instruments and vocals is highly dependent on the venue your band will be performing in. For a small pub, coffee shop or restaurant with tile floors you won't need as much amplification as you would say on a large outdoor patio or outdoor amphitheatre or a larger indoor venue such as a large ballroom.
My band plays primarily in smaller indoor spaces and occasionally at small outdoor parties. A small multi channel mixer driving PA speakers will handle multiple vocal mics, acoustic guitar, digital piano and electronic drums. I run all vocals and acoustic guitar and Roland Electronic Drums through the PA.
Acoustic drum kit is often loud enough (sometimes too loud) to get by with little to no amplification. If you need to mic certain parts of an acoustic drum kit you can use mics designed for that purpose on boom mic stands. Most of the venues I play in do not want the music super loud (and are acoustically lively) so an acoustic kit would be overpowering. The Electronic Drums allow for the volume of the drums to be adjusted to fit the needs dictated by the venue and the other instruments don't have to be turned up to match the volume of the acoustic kit.
In my band the electric guitar and electric bass run through their own individual amps. A Bass Amp will cover a wide area (low frequencies being less directional) and electric guitar amp makes it easier to dial in certain electric guitar tones by having both a clean channel and one for distortion. If we play a room that is L shaped and have to point one PA speaker down each of the two sections, I will usually mic the Bass and Guitar cabinets or plug them into a channel on the mixer using a direct out from the amplifier. Not all guitar and bass amps have that capability, but my musicians have amps that do.
The next consideration is whether to use a powered mixer with passive speakers or a passive mixer with powered speakers. The trend seems to be going towards powered speakers with a non powered digital mixer. For a four piece band you should get at least 8 channels. More if all your musicians will sing harmony or take turns singing lead. Consider that an electronic drum kit will use two channels to run in stereo. Same with digital keyboard. Microphones will need XLR inputs so be sure your mixer has enough for the number of mics you will use, including if you mic any guitar cabs or portion of an acoustic drum kit.
I recommend a 12 channel non-powered mixer with powered speakers because you can expand your PA system to accommodate various size venues with varying sound reinforcement needs. In other words, you can start with some smaller powered speakers for smaller venues and later add higher wattage speakers to cover larger venues and even run them all together in series. The same non powered mixer can send a signal to a variety of different powered PA speakers.
You might also consider floor monitors for yourself and bandmates. The PA speakers will direct sound towards the audience but your musicians (particularly any vocalist) will need to hear the mix in detail and a monitor facing the band will make it much easier. Some of the line array PA systems ("PA on a stick") are designed to be placed behind the musicians to allow both the musicians and audience to hear the sound from the speakers.
The self contained PA systems such as the type Bose made popular (but now close to a dozen other manufacturers have a version of) are primarily designed for one or two musicians with vocals and don't have enough independent input channels for a four piece band with four vocal mics but you can also use a non-powered mixer to enable more inputs into those systems. For a small venue a "PA on a stick" line array could potentially run your vocals and acoustic guitars and your electric guitar and bass could play through their respective amps. The line array can serve as the monitor for the band and eliminate the need for separate floor wedges.
Another consideration is weight and and the ease of set up. The newer powered PA speakers are actually much lighter than many passive PA speakers. The more components your system has, the more time you will spend setting up and breaking down.
That is my two cents worth based on my personal experience. You might visit some of the local music venues near you to see what other bands are using and interview them during their break to ask why they use what they do and if they would do anything different if they were to make a change. You will also be able to experience first hand how their system sounds.
I really enjoy playing with a band and encourage you to give it a try yourself. Good luck and have fun!