This is a great question and the answer is easy. You should run as many of the instruments as you can through the P.A.. It’s the best way to get an even live sound when your band plays. There are a lot of advantages to having everything running through the P.A. and it’s a must if you have a live soundman.
The biggest advantage of running everything through the P.A. is the fact that you have a central location to control the overall mix of your band. Your soundman can’t do much if all the guitar amps are running louder on the stage than the singer coming through the P.A. and the soundman can’t control them. It’s essential that you have a microphone on all the guitar amps and all the drums. The Bass can usually get away with running a line-in directly to the board. Just make sure if the bass player is using any effects, that the effects chain is also being run into the board. In a bigger venue your guitar amplifiers will sound many times better if they’re being pushed out the P.A. as well as being run from the stage.
Another reason to run the guitars through the P.A. is the fact that guitar amplifiers are very directional. Guitar amplifiers also have a focal point where the amp is loudest. That means the amp usually sounds great about 15 feet directly in front of it but then the sound gets lost or washed out on the sides of the stage and beyond the 15 feet. If you mic your amplifier and run it through the P.A. then the P.A. can spread your guitar sound out resulting in fuller sound.
There are advantages to running all the drums through the P.A. as well. It’s surprising how quickly you can lose your drums amidst the high volume of the amplifiers onstage. When you mic all the drums then you can add some Equalization and Compression to them to really make them pop in the mix.
Some more advantages to running everything through the P.A. are the fact that you can add Compression, Equalization and a Sonic Mazimizer to the overall mix. You can also lower the overall stage volume which means your ears won’t get fatigued as quickly. These things will all make your band sound better. We all know that the better your band sounds, the more people are going to enjoy hearing you and that results in more gigs.
I’ve written some articles that are directly related to this one and reading them will help you on your way to getting your P.A. and live sound setup.