I used OS/2 as my main operating system both personally and professionally between 1992 and 1999 (so, mostly the 32 bit versions of OS/2 rather than 16 bit), and still have it installed on real hardware and in a VM.
It does have some decent parts, but to be perfectly honest I would run it in a VM these days. There's very little software that needs to be run bare metal. Gaming wise there's little that's worth playing in OS/2 : Galactic Civilisations 2 is an excellent game, and is where the series originated. Avarice was interesting but flawed. I heard Links was excellent, but it also existed on Windows.
To answer some of your questions, and others you haven't asked.
Newer drivers can be downloaded to make the AWE32 work
For multi booting operating systems, always use the OS/2 boot manager. Never use its dual boot on a FAT partition facility, it doesn't work well. If you run OS/2, you should be using HPFS.
OS/2 supports large disks, the limitation is on the boot partitions being within the first 1024 cylinders. My retro PC runs DOS, OS/2, XP, Linux, and OpenBSD together without an issue. DOS needs to be on a primary partition, everything else supports logical partitions.
CDROMs work fine, but you later drivers may be used. The DANIs drivers are much better than the stock offerings.
To run modern OS/2 software, you'll need to patch Warp 3 up to date including the latest Warp 4 kernel. Once one of the latest Warp 3 fixpacks (thirty something) has been applied, Warp 3 kernel is brought up to the level of Warp 4, and Warp 4 kernel fixpacks may be applied. This does not apply to the other subsystems (networking), which stay on the Warp 3 track - not that this makes too much difference, because all but the server or post retail offerings of Warp 4 are still on the 16 bit networking stack. The workplace shell is not updated, either, but there's enough third party options to work round the minor Warp 4 enhancements. Speech recognition isn't worth it, and OpenGL is useless apart from running one package of screensavers - it is never GPU accelerated.
It's possible to create a bootable fully patched OS/2 install CD, but this works best on OS/2. It's supposedly also possible to do this in Windows - never tried.
You could buy a copy of eComstation, or the upcoming Arca Noae ArcaOS/BlueLion (coming Q4) and run OS/2 on modern hardware with much less hassle than shoehorning something from the mid nineties.
It is possible to install Warp 3/4 from floppy, but you really don't want to. If for some reason it's completely impossible to read the CDROM within OS/2, it's possible to copy all the install files onto a hard disk partition, and use that as a source. It's best to get the CDROM working though, as otherwise the networking install will be a little painful.
I may look at writing a document on how to install Warp 3/4 in a VM, but really, unless you're a die hard fan with a large amount of legacy software, and like using it as a boot manager (like me), why are you bothering with real hardware?