I have a Tundra,
I would recommend a 10,000 trailer in the 18 - 20 ft range with brakes on both axles.
Avoid the tilt model, it's too heavy.
You will need a Weight Dist hitch ( I use one).
You will will need a brake control, if not already equipped.
Please realize, not all Tundras are the same.
Mine has every piece of tow equipment that Toyota offers, to include a heavier rear axle(larger ring & pinion & larger wheel bearings).
My tractor is about 5,000LB, add the trailer add the extra people & gear, you are at the limit of the truck.
Mine tows fine, keeps up with traffic (if I choose to), stop very effectively.
A lot of people think you need a 3/4 ton or larger truck to move a riding lawn mower, that is just not true.
Shop around, talk to the trailer builders in your area, you can find what you need.
Bottom line, do your research, respect your truck and be safe.