I'm trying to form a band with couple of friends. We got drummer, basist and a chick on vocals, I'm the guitarist [yeap, only 1 guitar].
We're just about to begin playing together and I've got few questions:
What we may need to have besides the amps and the mic ?
Any suggestions or advices ?

Also we have pretty different styles:
Drummer is a huge Linkin Park fan.
Basist is in power-metal
Vocals: screamo but she's good at rock singing
Me: classical rock, blues lover.
Is this possible to connect those styles :>?

Poor polish guitar player.
It's possible to connect any styles together as long as the people all have a bit of give and take to them. You have to know when to surrender and when to really push your point. Always remember, an album is made of a ton of different songs. You can always write them all in your own way.

Likely you're going to need a lot of speakers for those amps and microphones. Otherwise just get yourself to the practise stage and get yourselves ready to start gigging.

Would suggest you each pick one cover from a band you like and you all learn them. There you have four different songs of varying styles to work with and see where your strengths lie, then play to them.
Of course you can mix those style, as long as everybody is prepared to compromise and doesn't get to much ego.
There's probably a way to do it, though if you're gonna play bluesy classic rock you might as well try to center around that and throw in other stuff on the side... actually if you can manage to combine blues-rock and screamo and do it successfully you would be my hero. But if you plan on doing that then you might as well get a second guitarist.

If not, see if there is one common thing you can all play and go with that for a while, your drummer and singer seem to be on kind of the same page and screamo guatar/basslines aren't quite as complex as blues-rock and power metal, so you might want to try that at first and screw around a little with mixing some genres. Just not the power metal.
Studies have shown that 92% of guitar players are close-minded. Copy this into your signature if you're part of the 8% who enjoy rap.