I am new to bow hunting and I am getting my stuff set up and I was wondering what factors are important to consider when purchasing a bow trigger release system?"
As other aspects of Archery, there is no rule of the thumb to choose release aids.
I don't use trigger release but a back tension one. If we compare all types of release aids, you would have a few different options to try and choose from but narrowing down to thumb/trigger releases, I'd say the best you can do is to try a few different ones from friends that use them. Archery shops could also have a few to try.
Personally, I'd go for the cheapest to start. :)
Since you are interested in bowhunting, I would recommend a thumb or a trigger release.
Most people acquire an index trigger release when they are just starting out because they can be had for as little as $25. Archery shops sell tons of these. They allow you to find a good form, rhythm, and release cadence.
While I have had good experiences from index trigger releases from the couple of manufacturers I have tried (Tru-fire, Easton), I saw the following problems:
While hunting you may find that the index finger release feels awkward attached to your hand. It might make you itch and scratch, or simply a clumsiness factor you don't need in the tree stand. On the positive note however, there's little way it can break or fail, and it's strapped onto your arm so you won't drop it.
Enter the thumb release. The thumb release, counter to the finger release, is not strapped to your hand. You hold it in your hand or you can hang it from a D-Loop knock in your bow. I prefer to let it hang from my string where it will be ready to go, and my hands are unobstructed for grabbing a snack or reading a book.
I definitely find the thumb release to be more accurate since moving the thumb contributes to less of a steadier shot than the index finger. Try both a finger and thumb release, and see if you notice a difference in your follow-through after loosing the arrow..
If you decided to bowhunt with a traditional or recurve bow (which some might not recommend due to the lack of poundage and let off of a compound bow) You might research some kind of a leather arrangement, but I wouldn't know much about these within the sport of hunting that you would consider. You may want to consult a community of traditional/recurve bow hunters who can share their experiences, or find out for yourself.
Keep in mind you will want to consult a bowtech to establish that you have a fitting and safe bow and arrow combination before establishing your preference for release. Some people shoot compounds with no release at all, but this is less common in bowhunting, generally speaking.
Side note: I'm sure there are some purists that believe that shooting with a release is an unnecessary addition, further mechanizing the compound bow. If it has a trigger, does it become a gun? I think the answer is obviously not, and many would agree. The use of a release, glove, or guard is a prevailing choice in archery now and I would assume throughout most of history. Have fun trying out different releases. I'm sure you will find what feels and shoots the best.