[RPG] What benefits or powers does a cleric gain from choosing a deity

The third edition of Dungeons & Dragons gives rather extensive rules for god creation in its Deities and Demigods. The net effect is that worshipers make the difference between a being with divine rank 0 and divine rank 1; more information about that can be found on the d20 SRD here. AD&D had its own Deities and Demigods book, according to Wikipedia, so that may describe how it works in AD&D. I feel I should also note that the webcomic "Order of the Stick" was originally making fun of 3.5, not AD&D.

The answer is Yes, there are restrictions. Check with your season to make sure there are no exceptions. The general guideline is:

From the "adventure league's players guide" by WotC in the Section:

"Part 1: Characters" => "Character Creation" => "Choose a class":

Deities. D&D Adventurers League storylines are set in the Forgotten Realms, and as such, people worship the deities of that world. If you would like your character to worship a deity, you can choose one from the list of Forgotten Realms or nonhuman deities presented in appendix B of the Player’s Handbook or the D&D basic rules. Clerics and characters with the Acolyte background must choose a deity from that list. If you’re a cleric, you can choose one of the deity’s suggested domains or the Life domain. The Death domain is not allowed unless that rules option is available for your storyline season.