What is your budget?
Among bookshelfs, the BMR is a stand-out for value, providing great SQ per dollar and as much bass as you can expect from a bookshelf. However, I don't know why you are buying a bookshelf, and the BMR is a very large bookshelf speaker. Similarly, the Affordable Accuracy is a class leader in SQ and bass extension for its price.
If you know you want neutral and accurate sound, I would get whichever best fits your budget, then decide if you need a sub.
If you need a sub with either of these speakers, I think it is very safe to say you would need a sub with any bookshelf speaker you might buy, so there would be no regrets on that count.
A little advise:
Some speakers are designed with extra emphasis on bass to off-set the lack of extension. One of these speakers may be more gratifying to you than the Philharmonic options (which are neutral through the bass they produce). Just be aware of that possibility as you are listening.
Some companies, such as DefTech and Canton (to name two), exaggerate their frequency range. By most accounts, both are competent speakers; however if you are looking for a speaker with deep bass, these will look good on paper, but be lacking in actual performance. If that is a major criteria in your search try to find reviews with test charts, or ask here. If a 6 inch woofer claims to produce 24Hz, something is not right!
If you decide you need a sub, and money is tight, you will be able to get away with a cheaper sub if you do not worry about playing a 16Hz organ note. A sub that rolls off around 35 Hz in an anechoic chamber will likely get into the upper mid-20Hz range after room gain. A sub like this will fill in a lot and save the speaker from playing notes that push its limits. It will cost a lot more if you start chasing those very rare lowest notes. I am linking to this sub because it is currently $190. When that sale is over, it is no longer a good option.
https://www.jbl.com/SUB+550PBK.html?mrkgcl=741&mrkgadid=3305175206&utm_campaign=Con|Text|Products&utm_medium=paid-search&utm_source=Google&utm_term=sub_550p&utm_content=SUB+550P&adpos=1t1&creative=312519824396&device=c&matchtype=e&network=g&gclid=Cj0KCQiA6dLgBRDoARIsAJgoM4uJaiJUNyE66qfH9XEtfpyFWyNDTErrDdyVQffJ54jwMJL2LXpZQ-caAokoEALw_wcB