How can I find a FNM-competitive affordable deck?
In the current standard, a few decks I would look for are UW control, Mono-blue Brains and BW control. UW control utilizes white sweepers and blue counter magic.  Mono-blue brains is a control deck that tries to play sorceries at instant speed. BW control relies on spot removal to keep the board clear.

Another site you might want to check out is StrictlyBetterMtg's youtube channel. He does a lot of deck techs, with a fair number of them being budget. 

Reddit also has good resources, with a particular subreddit for budgets: budgetdecks

For format information check out another question: Magic The Gathering: Where To Begin