I've been using fleets of tiny ships for a long while now. I don't have much incentive to go bigger. Tiny hulls give me the most weapons per point of logistics, and they have no maintenance.
I really am not getting the incentive to go big like I did in GalCiv 2. I'm not getting that much more space each time I go up a hull size, and many ship components get bigger the larger the ship hull is. In fact, I would argue that I lose space when I go with big hulls. When I try to make a fleet using bigger ships, I lose firepower (assuming firepower was my only concern). I've also had lost some stats on some of my ships as 'better' ship components required more room resulting in me having to remove something to make space.
Money is also important. I find that funds are really tight. Its hard to have many things with maintenance costs. Hard to maintain a navy with large ships. If someone knows a way to get more funds, I'd love to hear it.
Regarding hulls, I've utilized the tiny ship strategy as well. I would combine those ships with medium class support ships to up their defensive stats and offensive stats further. It worked quite well until the changes to the tech tree with retribution took away some of the support modules. The problem without them is that the fighters typically suffer fairly heavy casualties. Replacing them fast enough can be a problem. For example, it might take one turn to build that tiny fighter with three firepower, but if I can also build a medium class in one turn that has what is likely to be at least twice the fighter's firepower then I can replace firepower faster with the medium class. Combine that with the higher defensive capabilities of the medium hull (more shielding, armor and point defense) and more hit points and the calculation becomes more certain from my point of view. So I can fill out a fleet in fewer turns for roughly the same firepower, more defensive capability, and higher survivability by going with medium hulls. I rarely go past medium hulls, however.
Regarding economics I just don't see the challenge. I typically play on gifted level for the galaxy setting with all AI set to genius. Even with an economically crippled custom race (high maintenance costs, lowest economic rating, and lowest popularity rating) and not getting Paxton's emporium, money just isn't a challenge. All it takes is the consulate building either adjacent to another consulate or influence generating building and you can be making hundreds per turn very early and thousands by mid game. I have single planets pulling in tens of thousands per turn and my treasury maxes at 1,000,000 on a regular basis. My issue is that with the choices I've made for my custom race I should be having money issues.