B-Balls,
Your dilemma is one that many have struggled with because all 3 of those are worthy options
I'd say for your stated use, the best option is the Bushmaster Patrolman's Carbine. I'd add - the A3 version is the best configuration.
why?
1. the M4 style is hands down the most popular and biggest seller. This will ensure parts into the future- no problem, re-sale value - if ever necessary, and it so closely resembles our military M4
2. Bushmaster has excellent customer service
3. Bushmaster has so much in the way of accessories and generally supports the product well
4. The BM over the RRA since it has chrome-lined barrel/chamber standard. With RRA, it is an option
5. The A3 since it will give you unlimited options for optics, accessories etc. that the A2 will not (A3 is the flat top version)
And lastly, pricing. RRA and BM P-carbine is priced about the same as the comparable RRA, and offers the above advantages.
Not to waffle on my postion, but if you went RRA, you would have a great AR15 as well. Fact is, the differences are subtle. There is not a bad choice here.
Good luck with your selection, and let us know how it works out
Happy New Year!!