I would like to create a new race which you can play as a PC without it being too overpowered for normal game settings. I would like one with wings, but are wings (even wings with clumsy maneuverability) (or gills or claws or a prehensile tail) potentially game-breaking? And what about racial traits and size categories and spell-like abilities-which ones are acceptable for PC use?
There is a race builder tool/process that uses a point-buy system similar to point-buying for stats. Alternately, the easiest thing to do I find is to "re-skin" something existing or a sample race in the race builder; give it a different name, a slightly different assortment of features, etc. Try looking through the expanded race guides to see if something already exists that's close to what you want, then adjust it as needed.
You can also use the Monsters as PCs rules to use a creature as a player character. The creature's challenge rating (CR) acts as an effective class level, so if you picked a winged creature with a CR of 1, that is on a gross scale equivalent to a 1st level character of a PC race. It would have no class levels, but it would level normally beyond 1.
I say "gross scale equivalent" because many monsters, even CR 1 monsters, can be tremendously unbalanced.
The trick in the CR 1 case is to find something that flies and has a brain and isn't totally unbalanced for 1st level play (like the pseudodragon; that little guy's CR 1, but has a ton of powers compared to a 1st level character). A nixie is an example of an aquatic CR 1 creature, but again, it's got a lot of powers that make it unbalanced at 1st level play.
At higher level? A pseudodragon sorcerer or nixie druid might be perfectly fine, because their abilities aren't unbalanced compared to higher-level characters (by about 6th to 8th level, in my opinion, neither of those races' powers would overshadow the other PCs, who are also 1 level higher).