The wire from the cicuit breaker
I agree with the #10 unless the dryer is like 100 feet from the electrical box(very unlikely).
The standard house dryer circuit is fused at 30 amps and is wired with number 10 wire (no. 10 wire is rated at 30 amps). I've wired many of them in my life, including those which are checked by the county/city inspectors.
Agreed. 10 ga. You could use 8, but it would be a waste of money and it is much harder to work.
Dryer is 220V and usually 30 amperes. Go with 10 gauge or larger (smaller number).