Hi!
Troop transport and Spore ship are the only two means to directly hit their planets. The indirect way is you can use your influence to culturaly "flip" their planets.

BR, Iztok

Ships only attack "things" in space...other ships and starbases. No, you can't just attack/target a planetary improvement. As you probably have guessed, the best way to go is with an attack force of fighters/battleships first, then a fleet of transports. The good thing about a fleet of transports is that you can attack with a huge army but you only "lose" the ships that the lost soldiers were from. Example: 10 ships of 2000 troops (assuming you have researched advanced troop mods) lets you invade a planet with 20,000 soldiers; if you lose 2,610 of those soldiers, you will only loose 2 ships (the 2000 from the first ship and the 610 from the second...your new planet pop will be the remaining 1,390 troops). You will still have 8 ships of 16,000 troops to attack the next.