Alot depends on if you are using "personal defense weapon" as a general term or if you are actually talking about a PDW. Also depends on what you already have and what your more specific intended use is for it. I'm going to assume you want some kind of rifle or carbine, LMK if that's not the case.
If you have absolutely no rifles and need a "Jack of all trades" rifle, I'd lean towards an established brand AR-15 in the standard 5.56/.223 with a low magnification optic (1-4, 1-6, 1-8). It gives you the versatility to use it for CQB and also reach out of you need to.
If you are looking for a simple Pistol Caliber Carbine, the KelTec Sub 2000 is an option. It folds down pretty small so you can stow it and you can set it up to take Glock, M&P, or CZ mags at least, I think there are more kits too. The other options I'd lean towards would be a purpose built 9mm AR that takes Glock mags. Even if you don't have any Glocks, the mags are crazy plentiful and inexpensive.
If you are talking about the actual PDW term, I'd look at an AR (or AK if that's your preference) pistol in either 9mm or 5.56/.223 with a pistol brace. It's a nice compact setup that is easier to handle for most than a shotgun and more accurate and intuitive than a handgun. Going with a pistol brace setup avoids having to pay the cost and do the paperwork for an actual SBR. Toss a red dot on there and they can be a beast for CQB. Lots of options out there, if you want more specifics LMK.