Actually, unless the code isn't working the way it seems to be supposed to, fleet composition is entirely based on the supplies and crew that are inside of a station. Each station basically looks at how much supplies and crew it has, and then builds the biggest fleet it can with how much supplies and crew it has, subtracting those supplies and crew. When a station has just gotten a supply shipment from freighters, it is usually able to make a larger fleet, while a station that hasn't obtained a supply fleet in a while is left making rather small fleets. A faction that has gone a while without any warfare is usually able to build several large fleets before it runs low on supplies because of the supplies that it has been able to save up. I believe that the fleets don't get gradually bigger with supplies, but gradually smaller as the supplies run out, until the station receives another shipment at which time it is able to make larger fleets again.
Also, another suggestion to maybe help you with the early game before you can get a fleet, you are able to buy supplies and crew (and on very rare occasions, a weapon or two) from stations that do not belong to you and sell them to your own station to help fuel its fleet production. This will result in a net loss of money for you, but it will allow your station to build more fleets that it wouldn't otherwise be able to make, which can sometimes be especially useful.
Oh, and another suggestion for the mod, how about factions which have a station near an asteroid belt be able to send out lightly defended mining fleets for an extra supply boost.