what is a good size to start out with ?
I’d suggest 600lbs, but actually try flipping it before you take it home. I’ve run into tires that only weighed 600, but were nearly impossible to flip (rounded edges, no handholds, etc). Also see if you can get it weighed. Personal experience has shown me that people are off by about +/- 200lbs when it comes to estimating tire weights.
What’re your dead/squat numbers? There’ll be a loose correlation there - if you’re deadlifting around 400, you can probably flip a reasonable 600-700lbs tire a few times. 400-500 would be good for GPP style work. 800-900 would be a great challenge tire to work up to.
As pmb said, though, tires of the same weight can vary in difficulty.
Depends as well on your goal. I use my 250 lb tire for more explosive flips done for time and the 600 lb tire for strength emphasis for sets of 3-5 reps.