I'll shed a little light into the progression ladder for favors here, since I've never said anything about it.
When you first start the game, your favors are Intermediate level. The more favors you complete, the harder they will become. Right now, they only go up to Very Hard, but that will be changing soon.
The type of equipment you receive is based on the level of difficulty the favors you are doing. That is, there is a pool of possible prizes for finishing an Intermediate level favor, a pool for Hard and a pool for Very Hard.
So, in general, you should be receiving better equipment the more favors you complete. You may however, never get exactly the item you are looking for, if you get unlucky on the prize selection. If that happens, and there is no additional way to get a certain type of equipment (like buying it from a faction boss), than you might want to consider joining an agency, since they have ways of transferring equipment and money around.