I think that as soon as players finish the main tutorial they should be presented with a Doff tutorial, something along the lines off this:
Hailed by a contact (Ferra?) who then gives you 3 or 4 preset Doffs. He then talks you through the interface, but one with special tutorial assignments and not the normal ones. These assignments could be set to help a new character get on their way. You get a quatermater and a requisition assignment to go get some white/green level 2 hand phasers, you get a science officer and a scan mission to get a few items to start crafting, that sort of thing. You should also get the recruitment mission for your first set of random Doffs. Once all assignments are underway the tutorial ends and you can carry on with the game, and once they are all completed and you have your first batch of Doffs from the recuitment assignment the full Doff system opens up for you.
New F2P players aren't gonna have an uncle/aunt VA to buy/sent them little presents to get them started, so any help the game can give them will be much appreciated. It's F2P so players who find the first few hours frustrating have no investment in the game lose, they can just walk away and uninstall STO