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Now there's a wide-open question!
I'll try to take a high level pass and hope that's what you're looking for. If you know all this already you can skip to the brand name war that's sure to follow
If it's all indoor stuff, I'll start from the position that a pair of 8 ohm mains (15" 2 or 3-way) and a pair of 8 ohm monitors (I recommend 15's here as well) will cover the average blues bar set-up. Adust gear upwards to taste. You may want to include a powered sub as well, but I'd say that's optional. You'll need speaker stands... get 2 good ones.
There are lots of competitive products for speaker boxes, and you'll pretty much get what you pay for, but there are two generic options to think about: powered and non-powered.
Most sound folks I know argue that powered speakers sound better. They're certainly more efficient. But they also come at a premium cost that needs to be compared with other power options. The other thing to keep in mind is that you'll need to run house power (US = 120 volt) to each speaker, which can get cumbersome. They'll also require lots of extra XLR cables to connect them all together and to the sound board.
Non-powered speakers are more common, have been around longer if you want to find used gear, and, as the name implies, don't require power to each speaker... and they work just fine. They do require min. 14-guage cables and speakon connectors at both ends are pretty much standard these days. They also come in a huge range of quality, and here again you get what you pay for, usually.
If you decide on powered speakers, you'll need a sound board with at least as many XLR inputs as vocal mics, +1 or 2 min. extra. These come in all flavors and prices. If you decide on non-powered speakers, you'll also need a stereo power amp, typically split one side for mains and 1 side for monitors. Also common for non-powered speakers are powered heads, usually a combo of board + (at least) stereo amps built into a single unit. Again, most major brands make both powered head and non-powered products. You can debate brand names & quality in countless follow-up posts.
The only other immediate need is for mics, stands, and XLR cables. Here again I suggest not skimping on quality, as these pieces will all get heavily abused and you'll want gear that holds up.
A powered sub is costly but useful if you're filling rooms of more than 100 or so capacity Most powered subs I know of have built-in crossovers so you have a variety of options for sending signals through them. Non-powered subs are also an option but require an additional power amp and some form of crossover). All the components come with instructions for hooking things together and there are lots of generic manuals, but the truth is you'll have fun for hours figuring it all out. You should be able to fill the bill laid out above in the ball park of 2K new; considerably less if you're willing to buy pre-packaged kits and skimp on quality here and there, or just buy used gear.
I hope this wasn't WAY more basic than what you were seeking for info. There is typically lots of used gear to consider, including all kinds of rack-mounted goodies as you grow into a system. Have fun, it's great to be self-reliant and helpful to know how to mix from stage.
