Phosphate ones are just fine, just a little hard to clean (marginally, not so much it's a deal breaker). I've used a number of nitride ones and never had a problem with them, and I've used a couple of nickel boron ones, all with good success. Some guys have reported problems with nickel boron BCG, something about they're so slick that they cycle too fast or something like that, but I never experienced that.
So, Toolcraft is a good choice, they have a lifetime warranty and are easy to find (JoeBobsOutfitters, Toms Tactical). PSA Premium BCG's have been very reliable for me, I've never had a bad one. I think they're made by Toolcraft and one other manufacturer who also has a very good reputation. Sanders Armory sells a BCG that some have reported some staking issues with, but their nitride BCG don't have nitrided extractors, they claim it makes the extractor too brittle. Only BCG that I had problems with and had to send back was a Bear Creek Arsenal one.
HPT (high pressure tested) and MPI (mag particle inspected) are both very good things to find on your BCG, and those tend to be better quality.
PSA premium BCG's have both and are pretty nice. I have a Ballistic Advantage BCG that cost twice as much as my Toolcraft, but doesn't run any better or worse. AIM Surplus often has BCG sales, their EXO NiB is the onoe I used to buy and had good luck with. Don't get suckered into the whole " I need to buy the $200 BCG with the fancy logo on it" because wuite often they're made by one or two major manufacturers like Toolcraft, and you're just paying extra for the slick logo.
Full auto bolt carrier groups are very common and much preferred, mostly because they have more mass and help the rifle cycle reliably. If you get a lightened or lightweight BCG, be forewarned you may have cycling issues and you'll be experimenting with buffer weights and different buffer springs to get the gun to run right.