Traveller does have a reputation of being Accounts in Space...as this is a new game, i'm bypassing that part of things in the following manner (this is important as the players have their own ship, and those are expensive to maintain) But once the Selshor mystery has been solved, then they will have to start looking for ways to keep up the ship.
As for the financial state of things, in character:
The scientists are getting paid either by GLIPS or the Scouts, so for the next few months that is not a financial concern. The ship supplies (life support, maintenance, etc) will either be handled via the Scout bases on the way, or via the to-be-determined ship's vault that has a stash of credits in it. Dr Duk-Lyle is the only one with access to the vault, and it does carry significant cash reserves as well as credit sticks. The crew (Ferdinando, Franklin) are also currently salaried by the Scouts and GLIPS, again for a few months (not sure yet when the contracts will expire, and then you will either offer them a job or find new crew).