Mikegoob,
For something really different, a pistol caliber would do it. 300BO is interesting as a cartridge, but it's advantage is that it is just a different caliber for an AR. A pistol caliber AR is a fundamentally different arm. The choice of patterns for bolts and magazines is greater, and there seems to be a lot to figure out with each build. CMMG has a delayed radial blowback design that doesn't require heavy buffers. Another outfit, Macon Armory, makes direct impingement pistol caliber uppers.
I've built some 22lr ARs on the CMMG pattern. My sense is that it is the dominant standard for dedicated ARs in 22lr, the VHS of 22lr ARs.
Trueblue711 said:
.22LR is also good choice, but it's almost better to just get a S&W 15-22 vs getting a dedicated 22 upper. I got a dedicated 22 upper, but it's SUPER picky on magazines. I only found one that works. If I could go back, I would've spent the extra $50 and got the S&W 15-22. I hear nothing but good things about it.
The 15-22 has the advantage that you can take it out of the box and it should shoot reliably, without assembly or tweeking. It's also less expensive than a dedicated AR. The downside is that spare parts are going to come predominantly from S&W. Accuracy reports for the 15-22 range from not bad to pretty bad. S&W also has the Appleseed problem, which if you aren't going to an AS event shouldn't be a problem.
Dedicated 22lr ARs aren't problem free, but they offer a good range of choice for parts, and they can be easier to make accurate than a 10/22 imo.
If you are having magazine problems, S&W makes excellent magazines for the 15-22 that can be used in a dedicated "real" AR.