Get ratchet straps - 4 of 'em and some "soft ties" they are short webbing straps with loops at each end. Hook those over the bars, then hook the ratchet to them and the floor hook/rail of the trailer. The pull snug type straps will loosen up on you - I know this from experience and stopping every 50 miles to tighten them up.
Don't leave the kick stand down once you have it stable between the 2 front ties - it could break from pressure - the bike will shift a slight amount and appear to be bouncing some. As long as you have the forks compressed, it shouldn't go anywhere (dont ask how I know this!!)
I have used a UHaul bike trailer, no wheel chock but I tie it so the front tire is pulled/pressed up against the front rail of the trailer.
Then I tie the back tire by wraping the tied down thru the tire and snugging each side to the side rail - sorta a cross tie.
I have hauled mine 4+ hours a number of times. No need to empty any fluids (some commercial transports require that for their insurance reasons) - an almost empty fuel tank will just make it a little lighter, but I've hauled full too! Never a problem in that department.
I have only ever had one problem and that was not compressing the forks enough and it bounced when I hit a pothole coming out of a driveway - not a pretty sight. I have loaded and unloaded my bike by myself multiple times - a ramp tailgate is easiest, but I have done it with just a narrow removable ramp too. I did it myself the very first time it was tailered too!
You'll be fine.
B