the fat 1 is a push lock fitting it should have a plastic insert, that's your pressure fuel line to the engine,
the other is a vapor/vent tube and just shoves on the hard line, it retains no pressure.
I've had mine out a couple times over the years.
The only thing I do different is toss a couple short jack stands under the tank, so as you lower or raise it and is slides or tilts it'll only go as far as the jack stands. But I also apparently prefer to do it with a minimum of 3/4s of a tank of fuel.
Having the right tool for the job really does make all the difference. I tried balancing the tank on a piece of wood during the removal, which I quickly realized would be a p.i.t.a. Ran out an picked up a cross beam attachment for my jack that allowed me to really be precise when lining up everything as I re-assembled. Definitely worth it IMO.