Important first step....
Carefully read the game laws and regulations for the area he intends to hunt!
Many states requirements exclude a number of handguns capable of cleanly taking deer. Find out what is legal to hunt deer with, and then, make your choice from that list.
Also, conside the type of hunting he is going to be doing. Stalking in the woods is a lot different than hunting from a tree stand.
There are single and double actions revolvers, certain auto pistols, and single shot pistols capable and legal for taking deer under the right conditions and in the right areas.
The T/C Contender or Encore is easily scoped, and come in a huge variety of handgun and rifle cartridges capable of taking deer, and doing so at long range for a handgun. However, it is a single shot, and not what I would choose if I were hunting where the deer might jump from a bush 20yds away from me. For that, iron sighted revolver (or a magnum auto pistol) would be a better choice.
Don't fall into the trap that you NEED a .44 magnum. Deer, even the biggest muleys are not armor plated. A .357 you can shoot well is better than a .44 you can't. Since your brother is not an experienced handgunner, starting off with a .44mag may not be the best way to go. We like to think we are all manly men who can handle anything, but the truth is somewhat different. Starting off with something too big, too much recoil (and expensive ammo) means you can develope a bad flinch, and expensive ammo means you probably won't practice as much as you should.
There are a lot of variables involved, not the least of which is the ability o the shooter. Many people can learn to handle powerful handguns, over time, but very few are able to start out with one, and achieve the necessary skill to cleanly take game right away. On the average, it takes most people about 3 times the amount of practice with a handgun to match their accuracy with a rifle, at handgun ranges!
I use the paper plate method. If you can hit close to the center of a regular paper plate (no matter the range) you can put your bullet in the boiler room of a deer with confidence. IF you can do this at 80yds, then take that shot on a deer. If you can't, don't. If you can do it at 40yds, but not at 80, limit your shots to that closer distance, until you can do better on the range.
Practice, and specifically practice shooting from field positions is important.