I play Single Player, and mostly the map dictates for me. All of my games are large FFAs (typically me and 9 Unfair AIs). So with a little diplomatic luck, I can make sure that I only have one front open at any time, and then I just need one fleet that I can split up or combine depending on how I want to attack. So if one enemy planet leads to two others, I can split my fleet in half and attack both, then join them up again and keep going.

But other times having one fleet is suicide because you can get attacked way on the other side of the map, and unless you're Vasari with phase gates you can't get back there in any reasonable time frame to defend so you need a second fleet to defend or keep them busy on that end.

I have been keeping 2-3 fleets lately (large + maps, ffa, 8 AI players) . When I take over my first system, I'll park the large fleet at the jump area for the next system I'm trying to invade. I then move my strike fleets around the enemy areas and zerg the undefended planets until the AI attacks them with a larger fleet. I'll then jump them to another planet and start over again. I use my primary fleet to control and wipe out the planets around the jump area or jump back to my system to defend if the AI moves past my primary fleet.

 Regardless, you need to heavily fortify the planets around the system jump areas. so they will keep the AI occupied until your primary fleet can arrive to engage them. It's a pretty fluid mix of offense / defense, but has seemed to work very well in my last few matches.

~ Scards

I play minimum phase lane maps, so I play with 2 blocking fleets (depending on how many block positions I need at the time), a Strike fleet, and later in the game a follow on fleet. The follow-on fleet always holds the last world I took, so that ships jumping behind you as you jump in, cant destroy the planet I just colonised. Depends a bit on how many block points there are, and how actively they get attacked.

Early on, I use a colonise fleet with an Akkan and support to run around the militia planets collecting them, while I build a proper strike fleet. Once I've discovered the main enemy positions and the block points, I do block fleets for each block point, then work on a strike fleet. The Akkan fleet is usually running around behind me at this point colonising planets in "my space" that got bypassed to get to block points as fast as possible.

One large fleet and a couple of TEC colonizers with 'armstice' (shuts down the fight long enough for the big fleet to arrive would work also

If you have powers to keep your opponent from leaving before you carve a piece out of his hide or powers to reinforce quickly (read, RA), one big fleet can do quite well.  If you have one large fleet (or mostly one large fleet), you NEED durable defenses (example, planetary shield, 2-3 repair facilities, 6 fighters worth of fighters, and some guns).  You also need to play differently.  Your big fleet gives you advantages, but requires a different play style.  Smaller fleets, you hit where it hurts and either reinforce and defend with repair to back you up or exit.  Big fleet you need to sweep through with your juggernaut, leveling everything that could be used to rebuild so your front lines are as small as possible.   You also need more static defenses on your front lines and you need to be willing to sometimes lose 1... 2... maybe 3 systems before your big fleet can eradicate their medium fleet.  Notably, in exchange, you can have a smaller total fleet size for a better econ. and still bring the larger fleet to any given engagement.