I’m still playing STO, although my time is very limited.
Things you cannot ever change, as far as I know:
- Faction (Fed vs Klingon)
- Career (Science vs Engineering vs Tactical)
- Species
- Gender
- Traits
I think everything else is changeable, although changing your chat-handle requires cash. Other things can be changed via in-game mechanics, usually by spending Starfleet Merits (earned by completing missions).
Of course, you want to know how important each of those five things are.
Faction is probably easiest to decide. The Feds have more missions, more costumes, more content in general. The Klingons have more than they started with, but expect to grind PvP if you want to advance.
Career is crucial, but hard to decide. I recommend playing each until you played up into the Lt Cmdr rank. The starter Lt ship is too generic to get a good sense of the differences among the careers. Of course, the ships aren’t class-restricted; a Tactical captain can use a Science or Engineering vessel, etc. Because of that the different careers aren’t much different in space.
The real difference among the careers is ground missions. Each career gets different kits to wear. The kit is what gives you abilities beyond shooting your weapon. You get a good variety of kits through missions. Keep and try them all to see what career you like best.
Gender is entirely cosmetic. Choose as you like.
Species is cosmetic, except for the trait options.
Traits are small bonuses and sometimes penalties that can choose from. Choices depend on species. None of them are overpowered, but some might not be as useful. Even the best ones are only small bonuses. By the time you’re at a high rank, other factors will be more important.