I am pretty new to StarCraft 2, and I was wondering if there is a name or a way to search for StarCraft 2 games that start you off with a certain amount of resources and you are unable to farm any more. I feel this would be more like the Warhammer 40k table top game, as it would basically be a pure micro game.
Welcome to SC2!! :D
If you are looking to get started on a pure micro game, I recommend Marine Arena.
Technically its not pure micro, because you get money from killing other players' units in order to buy upgrades, but it is just about all micro.
(Btw, you do get other units than just marines)
As for a custom game which had a limited set of resources and you just 'played it out', haven't heard of one.
The game does not come with the type of game/map that you describe.
You can look for third party map. In Multiplayer, Custom games, you can "Join a Game" or "Create a Game".
These categories will be available:
The Custom category is the type of game/map. There is no fine grained way of finding what you describe from within the game client.
(note: the current game client is Version 220.127.116.1129)