It's not fun but I do it all myself, that way I get to tell everyone I never let another man touch my meat.
Are you asking because you've never done it and wanting to get started? Very high level overview, you'll break your animal down into quarters, backstrap/tenderloin, and neck/trimmings and toss them all into a cooler ASAP. I like to keep the meat on top of the ice to stay dry, but some intentionally soak it, you'll develop your own preference over time. Some people process right away, I wait 7-10 days or until convenient, usually starting the following weekend. I'll muscle out the hindquarters and freeze the muscle groups labeled appropriately to process later, sirloin, top round, etc... Using the correct names isn't important as long as you know what to do, I'll label stuff football or jerky, etc. Then I'll pull all the meat off the front quarters which is usually going to be ground. I'll cut steaks from the backstrap and typically cube everything else up in grinder sized chunks and freeze in large bags. I don't grind until summertime. You can keep the heart and liver, I like both especially on a younger deer but some guys will only keep the heart. The shanks are the best part of the deer, if you cross cut them with the bone-in they make great slow cooked foods with tons of flavor. I've been simply cleaning them up and freezing them whole and making pot roast with them either slow cooked all day or in the pressure cooker. Get on YouTube and watch videos "how to quarter deer" "how to muscle out a hindquarter" "how to process a deer" "how to use butcher paper to freeze meat" and stuff like that. You don't have a location in your profile but I always start people out on hogs because it's not a huge deal when they mess up, you'll butcher (not in a good way) the first couple you do, but the good thing is no matter how bad it is it'll always make good ground so not a big deal.
You're going to want a couple deep meat tubs and a boning or fillet knife, doesn't have to be expensive but you'll appreciate the extra blade while you're working. Take your time and go slow, you don't have to do the whole deer in a day. Do one hindquarter on day 5 and then watch some more videos on breaking it down and do the next one on day 6, etc.
I bought this knife a few years ago for $13 and it's great for the price for working meat.
https://www.amazon.com/UltraSource-Breaking-Butcher-Knife-Fluted/dp/B00JPE9OK4/
Meat tubs like this, probably just pick them up locally, I'm just using Amazon because it's easy to reference.
https://www.amazon.com/Academy-Sports-LEM-Economy-Meat/dp/B005QJGMA2/
edit: Since you asked about books, Rinella has some out that I'm sure go over it very well and they'll probably come with his Osso Bucco recipe for the shanks. He's the one that made that popular and now people aren't feeding the shanks to their dogs anymore. lol
Also read your post again about the ice chest. For whitetail usually a 75qt Yeti is what we use but a monster you may need more space. I think a 75qt Coleman probably has more internal space but I don't have one to compare. You don't need a high dollar cooler, the Coleman Xtreme Marine series I had a while back routinely held ice longer than our Yeti's.