...I have decided I need a corded drill
as a backup, or maybe as an addition.

I added a corded to my collection about a year ago, and I've used it a
lot. I got a reconditioned Dewalt D21008K; it was about $35 on eBay.
They're currently available for $45 + shipping at toolking.com. It's
only a 3/8" chuck, but that hasn't been a problem for me - if a bit is
larger than 3/8", it will go in the DP. I chose the 3/8" over the 1/2
both for price and the higher RPM offered by the smaller drill. (My
brad point bits are reduced shank, though, which makes a big
difference and lets me use them in the 3/8 drill.)
I looked closely at some of the Makita corded drills, as those were
also reasonably priced, but I just picked the Dewalt because I got a
good deal on it. I don't own one, but from what I've read, Milwaukee
is top of the line for drills, and they're priced accordingly.
Probably worth it if you'll use the drill all the time.
Another thing to consider is that there is a 1/2" Jacobs brand chuck
available that attaches to most 3/8" drills - that's Jacobs model #
31037.
Good luck,
Andy