morning, the 6=06 is a very good choice, but i would make 6-06AI definitely a screamer. rem. still makes 6mm brass, winchester use to, i have a 6mm, and a 6mmAI. very accurate. i was there 1966 Phu kat.
I'm in the middle of building a 6mm Rem. One of the reasons I decided to have it built (when I started the process about 3 years ago) is that 6mm Rem Brass was _EVERYWHERE_. One LGS had probably 60 bags of Remington brass. Right after Sandy Hook, even that disappeared.
I picked up a bag of about 250 once-fired 6mm cases and have winnowed that down to about 80 good cases. I did pick up 3 boxes of Federal Premium Vital Shock ammunition with the 100 gr Partition on clearance for $10 each, so I have those 60 cases of known history. Not that I'm really excited about Federal cases.
Gunbroker is probably the best place to look right now. That's where I had to turn to get 257 Roberts brass until Nosler did a run last year. You'll pay more on gunbroker, but they're available.