The cost of cable is very low, in relative terms. Get the highest quality cable possible. The goal is for that cable to be able to do 10 gigabit and beyond. New houses these days typically will be connected via single mode fiber, and fiber will capable of at least 10Gbps, and you don't want your LAN to be out run by your ISP's speeds.
I'd recommend that you run at least two runs of Cat6a (rated 500+MHz) to each room of your house. Run cables close to locations where you could potentially have TVs. Run cables to locations where you might want to distribute network access points in the future. If you want to get gear like Ubiquiti
in the future, having a power-over-ethernet switch in your basement powering the different access points would be a great solution for fantastic WiFi coverage.
For "wired" phones I'd probably recommend for you get some sort of VoIP phone, and those use standard RJ-45 jacks. I wouldn't bother with RJ-11 jacks personally.
In my current house we ran two Ethernet cables to every room, and there are no RJ-11 plugs. For a wired phone I just took a VoIP "ATA" adapter, plugged it into one of the Ethernet jacks physically near the center of the house, and have a wireless phone system plugged into that. Going forward, I sometimes wonder how much longer I'll even be using my VoIP setup. When I'm talking to someone voice it's usually using something like Skype, GoToMeeting, Google Hangouts, Facetime, or my cell phone.