Unless you have your heart set on a certain class or type of ship, firstly devise interesting and engaging characters and think about what stories you want to tell about them, then select a ship to match.
If they're explorers go for a Nebula-Class, soldiers go for an Akira-Class, scientists a Nova, workhorses a Miranda, etc. Also try to be practical. If a ship has 70 phaser arrays and 500 torpedo launchers then there aren't many hostiles they'll come across that will be a threat--unless they have 100 phasers and 800 torpedo tubes, in which case the UFP would be pretty screwed. They don't have to be on the best ship there is, when something a little more average will help ramp up the tension and make readers ask, 'how are they going to get out of this?'
The class of ship will also have a lot to do with your Captain. NuTrek notwithstanding, it is doubtful a newly promoted 30 year old captain would get command of a Galaxy-Class ship. Ships of that size and complexity would go to older, more experienced and seasoned officers. Such an officer might get a Sabre-Class or possibly even a Miranda, until they gain more time in the big chair and prove themselves capable of greater responsibilities. Look at Picard, he made Captain at 28 and commanded the Stargazer
for two decades before he was eventually given the E-D.