I played in stage bands (keyboards, bass, sing) for more than 30 years... I suggest you pick up a PA system. But there's a lot of shades of gray in that statement. Some larger bars will have a house system and they control the sound as others stated. That's cool - less to carry in and out. In addition to sound, some bars (I used to play in NYC's CBGB and Kenny's Castaways) also have a fixed kit bolted to the floor (you would hope your drummer is not lefty with the hat on the right side). Your drummer only needs to bring his favorite cymbals.
For small bars and parties and such you really just need a powered mixer (head), two bins, some mikes and cables. Most of my bands were 3 or 4 piece classic rock bands. For the head, we typically had a powered mixer with a handle (for carrying - many powered mixers are not for mobile use). Probably 200-300 watts is fine for small bars. Keep in mind powered vocals are VERY loud. This is similar to guitar vs. bass. A 100-watt Marshall head with 4-12s in a bar is painfully loud for the audience, but an Ampeg 200 watt bass amp with 1-15 needs some help. It's typically buried and maybe needs a cabinet with a horn or 2-10s over 15 (my fave setup).
In one band, we used a Peavey PV5300 powered head. Easy to carry, good for small bars.
For your bins (speakers), two 1x12 with a horn is fine. Bins with 15" woofers are big, heavy, and hard to transport.
Shure SM-58's are the go-to workhorses for bar mikes. They can handle a lot of abuse, drops, and spilled beer. Cables are cables - buy spares, they always go bad.
My most important advice... Buy everything used. Gig equipment takes a beating, and I've played some gigs where fights broke out. Everyone is drunk and the bar owner is going to pay you crap anyway. Don't spend a lot of money on equipment, leave the Les Paul Deluxe at home, bring a beater to the show that sounds good, and just have fun. hehe