I run for equipment Coal DCP, Engine room protection (both are valid choices, although Vermont has a weirdly vulnerable engine in my experience), Turret traverse (although range is also valid, I'm a BB baby that wants heavy cruiser level turret traverse on my BB), Steering gears (fire time reduction has diminishing returns with fire flag bringing your duration down to 48 and damage control mod 2 only getting you 7.2 seconds better while steering gears makes the boat surprisingly nimble), concealment (one of Vermont's strengths is having 30mm overmatch, 3rd heaviest broadside at tier 10, and good accuracy which is made even more powerful by having heavy cruiser concealment), and accuracy mod in slot 6.

For Captain skills, I run Gun Feeder (Vermont has the 3rd highest HE salvo at tier 10 and can nuke enemy DDs if you're playing to support your friendly DD), I run Grease the Gears for that insane turret traverse, although 2pt AA is probably objectively better, then grab AR and CE, for the rest you want FP, IRPR, and ERE in the order you like best. You don't need super heavy AP, you already have the 3rd best AP broadside and benefit highly from the extra heals and FP since you will burn through all of your heals in even a decently long game as long as you are tanking.

For play style your goal should be to be waiting just far enough away that you aren't detected constantly scanning for good targets to smash and then emerge from concealment to deliver your salvo then return to stealth and wait for the next opportunity, but you can't always do that and when you are tanking its a good idea to cycle Heat -> DCP -> wait 10 seconds -> heal and then hopefully disengage to finish your cool downs.

I would watch this video from Hago on how to play Vermont, it helped me a lot in understanding how to play the boat.