Sorry for the potentially stupid questions...

My first character is a Science Officer and was hoping to be able to dish out some serious damage further into his career but looking at the comparables it seems that the choice for a DPS based character/ship combination is a Tactical Officer + escort class ship... Correct?

If so, that would suit me fine as my favorite ship from the various series is the DS9 Defiant.

Also, are escorts really that much more maneuverable than the Miranda class ships or does improved maneuverability have more to do with increasing the character's skills and the ship's equipment?

Yes, Tac/Escort is your DPS path. But your weapons/ Boff layout affects that as well.

And your skills, consoles, and the ship's innate stats all affect your ability to zip around. I found the Defiant a bit too spinny so you may not want to crank the turn rate too much with a console.

I'm sure some of the number crunchers can give you better details than I.

The Miranda class has a turn rate of 11.4, while the Defiant has 17. Comparatively, the Defiant turns on a dime while the Miranda does a 3 point turn in the parking lot. Unlike the Miranda, the Defiant's stats were built with cannons in mind. While the Miranda can use cannons, the lower turn rate makes it much harder to get into the 45 degree fire arc that the cannons have. The Defiant has zero problems doing this.

I've flown both the Defiant and the Jem'Hadar ship (which has a turn rate of 20?) and I've never need a console to boost the turn rate.

And yes, Tac/Esc is the DPS route, though I've played Sci/Esc and still done decent DPS, just not as good

You may want to take a look at the mvae as well as it can help complement your sci abilities. It is the only escort with a lt commander sci boff station. The mvam with photonic fleet and scorpion fighters can be good for spam.

Please understand that your science captain would not have to fly a science ship and can fly an escort.

Agreed. I run sci captains on both KDF and Fed sides, both in escort-class ships. You do not need to rely on Sci BO abilities for primary damage. Instead, use tactical BO skills like cannon rapid fire, high yield torpedo, or whatever matches your chosen ship weapons load-out to deal damage, and sci abilities like tractor beam, jam sensors, sub-nuc, etc... to control and cripple your opponents. Rather than using brute force to overwhelm their targets, sci captains rely on debuffs to bypass their defenses.