Depends on your targets I suppose!
Pretty much the above. Nevetheless depends on where you are in the game, what your income is and, most of all, what ships you enjoy the most.
Early to midgame I usually run a frigate-heavy fleet with 1-2 cruisers, 4-5 destroyers (1-2 of those carriers), 10+ frigates and whatever support ships I can loot for fuel, cargo and crew. It's decent for fuel use, thus exploration. Also has enough space for ad hoc trade runs should a trade run suddenly become rather lucrative.
Mid to late game is when I establish my first colony, having explored a large chunk of the sector. That's when I begin upsizing, so I sell the Shepherds I have, replace lost frigates with cruisers or the occasional capital. By end game I usually run a carrier-heavy fleet with 5-6 capitals, 6-8 cruisers, 4-5 destroyers, 4-5 frigates and as few support ships as I can manage.
Still, once you get the blueprints and the cash try to experiment with different compositions. A full phase or high tech frigate based fleet can be quite insane for specialised battles. Drover spam is never not funny. And a full capital fleet's only issue is the cost.
Oh, and welcome to the Sector citizen!