LAST EDITED ON Feb-23-14 AT 00:49 AM (EST)
 
>I have a max character but I'm still fairly new to STO.
>
>Just got the Dyson science/tac ship and turned it into a missile boat
>since the aux cannons on my Vesta can't be transferred.
>
>What's the best Fed ship in the game right now?

Missile boats would be great if torps didn't have such annoying cool downs. I'd recommend a single torp with spread 2 or 3, then focusing on beams or cannons/turrets. Never mix cannons and beams. If you're worried about keeping your aux power high, buy a warp core that dumps weapon power into aux. Your gravity wells will hurt a LOT.

My fleet's pretty deep into ship crafting and for Feds, the best ship in the game right now is the Avenger. It's a really solid ship. Run it with seven beams and the Borg cutting beam you get from Omega reputation. You'll destroy everything. Runners-up: Excelcior refit, Vesta, and the Odyssey. If you're on a budget, you can buy a mirror assault cruiser on the Exchange really cheaply and turn it into a great My First Beamboat.

On the Romulan side, the Scimitar is still brilliant. Ar'Kif is nice too.

For Klanks, look at the Mogh. My guy runs a Mirror Vo'Quv with Advanced Slavers because I make money by selling Contraband on the exchange. I made enough to buy Thrawn a Bastion Flight Deck Cruiser recently. It's great.

Three quick notes:

1) Never play science ships. Science was nerfed hard just after launch and while it's somewhat recovered, the benefits of a Commander Sci station don't outweigh the disadvantage of only being able to run six weapons. Apparently a Science revamp is being mooted for Season 9? Watch this space.
2) Beams + their damage boosting consoles + Beam Fire at Will is a really solid strategy. Never mix weapon types or damage types. You will see a lot of players who do this. They are bad.
3) Escorts are fun as hell, but as the endgame content largely revolves around shooting large, stationary targets, it strongly favours the slow-orbit-in-a-cruiser approach. I generally level in escorts and then switch to a Cruiser at 40 or 50, depending on what's available. With that said, a Patrol Escort (Fedside) is even cheaper than a Mirror Assault Cruiser to set up to run STFs.

Edit: Fixed a couple of mistakes, added a third tip.