A 3", fixed sight K frame (M10, 64, 13, 65, etc) is the obvious answer - given the budget limitation.
That said, JohnRippert's (Post #29) recommendation of a 2.125" barreled M640-1, is a good one. 38 or 357. Mine wears a Hogue Centennial Tamer, & is hands down, the most naturally pointing revolver I own.
I also own a very nice 3" M65-3, & have quality Andrews Custom Leather pancake (Saddle Style) holsters for both. Although both conceal well, the M640-1 carries better, & usually gets the nod for a trip to the store - or a night on the town...
Pics of the M640-1 w/ both Hogue Bantam, & Centennial Tamer attached.
Regards - GCF