I can say that I grew up using a 5150 - in the 1990's. At my high school, the English typing labs had PS/2 Model 8525-001's (the mono screen with two 720kb floppy drives). The typing class had Novell-networked 386's, and the computer applications and programming class had 5150's with monochrome screens. In fact, we only got color screens in my sophmore year (1992-1993) because a former student donated a few dozen PCjr machines to the school, and my computer teacher soldered the 9-pin DINS onto the Jr monitors so that we had CGA compatibility, dedicating the rest of his class's funds for the year to purchasing the 35 CGA cards to put in the machines to work with the new color monitors.
We ran DOS 3.3 on the in the computer lab. We used Microsoft Works v1.05, DBASE III, and Lotus 1-2-3 v2.1 for applications classes, and BASICA/Pascal for programming classes. Later, for the Programming II class, we were given the option of using QuickBasic 4.5 and bringing in our own boot disks. This was because most of the guys in our Programming I class had already created our own DOS 5.0 boot disks so that we could run QBasic (we were allowed to do anything we wanted that didn't make noise once our work was through), so by the time we hit programming II, we were all familiar with the new environment, and our teacher was more than happy to allow us to continue.
(of course there was also Pascal 3.0 that we learned in ProgII, but I tend to gloss over that since Basic was what I found to be fun)
One of our guys even wrote an email message-base. Users could create a username and password, perform look-up of other students, send and receive messages, and log out. The system had a bouncing ball screen-saver that would turn on after 15 minutes of inactivity, and would go to the login screen as soon as a key was pressed. All in QB4.5 (compiled, of course), running on a 5150 with both 360kb and 720kb floppy drives booted with DOS 5.0.
I guess my point is this - the OP seems to want to run QB on his 5160. The 5150/5160 series can do a lot of things, and for the most part, memory isn't that great of a concern unless you're writing serious code. I think his main point is that he wants an OS - any OS - and he wants QB. DOS 5.0 booting a 5150 will leave you with plenty of headroom for most things in BASIC. If he wants more headroom, then back-dating to 3.3 would be the obvious choice, to me, as it will have the most compatibility with the programs he might try to run while still leaving plenty of conventional memory available after OS load.