I would never start an engine with out checking the oil first. If it be transit checks first flight of the day or loading up the next student for the 10th time that day
Personally i would do a first flight check then taxi to the fuel then a transit check afterwards. ie quick visual check nothing has fallen off and oil again and fuel contents. And you won't make many friends blocking the refueling point while doing checks.
Don't really see much point of testing the fuel striaght after refueling the whole lot is going to be mixed up so for it to be any good you will need it to sit for awhile to settle. This really isn't an issue if you are buying your fuel from Air BP etc. But if you are using mogas or filling from a home bowser i would be abit more careful.
MJ