I usually shoot just one a year. Between that, fish, and if I can get a turkey or two, that makes up the majority of our animal protein every year. We do get chicken throughout the year, but we haven't bought red meat for the freezer in nearly 2 decades.
Our season is in the peak of the rut. I shoot buck and doe alike, whichever shows up first. The only deer I had that tasted gamey was a big buck that I didn't butcher myself. I blame the butcher for not taking the care that I do when I butcher. It was a 70 degree opening day and we had two deer to butcher. We iced them down and dropped them off at a usually, very good processer (and friend). The big buck was 230# on the hoof and the backstraps I got back looked like they were from a yearling. That was the first deer I paid to have processed in about 15 years, and the last I will pay anyone to do.
Unless its below freezing and I can hang it and continue hunting; a shot deer is dressed, butchered and in the freezer in a couple of hours. I'll hang it, skin it, bone it, cut it and package it (including grinding) non-stop until its in the freezer. And I'm not talking primal cuts either, we pack it in 1# packages except roasts and loins. I trim virtually 100% of the fat and sinew and put nothing but meat in the freezer. I don't have the nasty fat/goo/glue stuff stuck to my cookware and rarely have to drain any ground meat that's browned for chili.
So... I probably put more into processing than anyone I know. Cow tastes better than deer; they're supposed to! But I do everything I can to make sure the deer is the best it can be.