Best ship size?

[Suicide Junkie]

LCs at first.
Later, a mix of BCs and DNs.
Late in the game, all Battlemoons (in fleets of 2 or 3) to minimize the micromanagement.

[Puke]

Heavy transports.

fill half with cargo modules. pack in engines, solar sails, ecm, and stealth/scattering armor. fill the rest up with as much organic armor or shields as you can fit, maybe leaving enough space for a point defense gun or two.

guard it with a couple minesweepers, and space-to-space combat ships, and go conquer some worlds.

[Puke]

honestly though, i usually use battleships as troop transports. same size, but you can put on less cargo and more armor/shields. 1/4 of the space devoted to cargo is usually more than enough to conquer a homeworld class planet, in the unmodded game.