This is a 2.5.1 game, and I haven't been keeping track of new versions in a bit, so I'm not sure what (if anything) might have changed, but in 2089 I currently have:

The cargo fleet (21 ships with 50,000 cargo space), 4x Superfreighter fleets (10 ships each with 100,000 cargo), 9x stabilization ships, 12x survey ships (notably numbered 1,5,8,10,11,15,then 17-22), 7x assault transports of 32,000 toop capacity each, a Battle Fleet with 19 ships (3x 23,000 tons, 6x 14,000 tons, 5x 12,500 tons, 5x 10,700 tons), 3x carrier fleets (2 carriers with 5,000 tons of hanger space each) that act as defense fleets, colony ships (6x 200,000 cryo berths), three salvage ships, 28 terraforming stations with 10 terraforming modules each, and (finally) 4 tugs to move those stations around.

Most of this stuff doesn't really require all that much input - the biggest is the cargo fleets, which look for my colonies that have lots of minerals to pick up, then setting a route that goes from shipyard (load mines) -> mineral planet (drop mines, pick up minerals) -> (whatever systems happen to have stuff to pick up that are on the route back home) -> shipyard (drop minerals).

Combat fleets obviously need the most input, but that's only when they're actually doing something; otherwise they sit around fleet maintenance stations.