You can start with pretty much anything, just check that there isn't too big of a difference in the launch bay capacities between the fleets as that can turn ugly quickly. What size do you prefer to play? 1000, 1500, more points?
Starting with a 1000 points, as an example off the top of my head, might net you an Imperial force with 3 basic cruisers (180
ppm or so), a battle cruiser for a flagship (250-300) and a squadron of Cobras or similar escorts (30-50
ppm). This gets you a solid leader (that could be a carrier), some workhorses for the line and an agile group of harriers to zip about the place.
For Chaos it's quite similar, you might take 2-3 fast gunboats to attack things and a heavy carrier like Styx to belch forth assault boats while cheap escorts like Infidels fill out the points and provide threats on the table.
Don't know about Orks, but for Tyranids I'd start with a
LD 8 Hive Ship with some durability upgrades (300-400) and some carrying capacity, surrounded by six escort drones (20
ppm or so) and six Krakens (25-40
ppm) because unlike other fleets, tyranids love escorts but can only take 12 per Hive Ship. The remaining points can then be spent on one or two Cruisers and various upgrades to the fleet. Alternatively, take two cheap Hive Ships and go nuts with escorts.
Have fun