Buckeyes look very much like production Reds, but they have peacombs. They're fair (not great or excellent) layers, and are strictly dual-purpose. They're also slower maturing. I think you have Buckeyes.
If you're a first-timer, with no adult roosters to keep the young ones in check, I wouldn't pick a Production Red. (And even if they're sold as Rhode Island Reds, most hatchery RIRs are actually Production Reds.) They can be very mean roosters. I've only had one good one, and my parents used to always buy the straight-run Production Reds when I was a kid, so we've had a lot of them.
I'd research rooster temperaments before you get a rooster and are stuck with him. Most of the fast-maturing, egg-laying breeds have pretty hormonal roosters.
Game roosters are the best rooster you'll ever have if you get one from a good line, but they can also be the worst if they decide to be people-aggressive.
Australorp roosters are supposed to be pretty gentle, and I love the hens. The roosters are a bit large, though. Faverolles are also supposed to be really nice.
Or you could get a free, older rooster whose temperament you already know. If you're not really into biosecurity, that may be the way to go.
(And for those of you waiting to jump on me for ignoring biosecurity, my neighbors on both sides have chickens. One neighbor about a mile away raises pigeons. I never had a chance of being biosecure.)