I'll add another vote for 16' being not long enough, I know because that was what I had. I had an
L3130 tractor open station with loader and loaded tires at the time. The trailer was a 16' 10k rated (well 9990 lbs) car hauler/equipment low boy style. At the time I was doing this I kept a logging winch on the 3pt, which sticks out very little - maybe a foot total, and either the bucket or grapple on the FEL. Sometimes I would set the forks on all the way to the front, facing rear and put the tractor over it. The forks would get strapped down separately.
10k was the right weight class for this size tractor. 16' was way too short. I ended up having to back it on to get the weight dist right, which is OK to do, but that was the ONLY way to do it, so there was no flexibility. All that and the grapple or bucket would overhang the rear by 6-18" (grapple was longer).
20' would have been perfect. 18' would have been at least a bit better. But you are talking about a RC on the 3pt. That means you are looking at something sticking out 6-7', and heavy putting a lot more weight out back which hurts your tongue weight.
In your case I would think 22' should be OK in a 10k trailer with brakes on both axles. But your question was what truck to pull it... Well you need to go through all that first to see what the load is like. I was somewhere around 7-8k total load with trailer included. You will be a bit more with bigger trailer and the RC. So you need a truck that can pull 10k for sure, and things like integrated brake controller would be very wise. There will be half tons that can do it, but a 3/4 ton will handle it for sure. 3/4 ton is what I have, though I no longer have the trailer.
I know having a super long trailer can be a real PITA in tight spaces. Another thing to keep in mind is that plans change. Down the road you may find you need to tow longer distances, more frequently where you will be happy you have a bigger/better trailer than you might have got...or the complete reverse and you can sell the trailer. If you might need to haul more weight then you should be talking 14k trailer and then for sure a 3/4 ton truck. So you need to evaluate what you might want to do later on as well. It is always a bit of a guess, but worth thinking through.