Go for Cat6A as a minimum as that is rated for 10Gbps over 100m providing you some future proofing.
As above, don't bend the cable too tight, but in a domestic environment, you don't have to worry too much about getting it spot on. Try to avoid running data cables in parallel to power lines, if you have to, put some distance between them to reduce interference.
Stick with UTP in a domestic environment. Shielding brings its own problems and has to be done completely end-to-end to work.
As above, don't limit yourself to one cable, whilst you have the walls open, run as much as you can squeeze in. I've got four to my lounge and I've already utilised all those up. Sure you can run switches, but that's extra electricity you have to burn up and if you want to get a bit more advanced with security, expensive when you have to upgrade multiple switches.