Trailer length - does that influence spot availability?

Yes, you WILL be limiting your choices, especially in Nat'l. Parks, State Parks, National Forest CGs as they are all old. When they were built in the 40s and 50s, people had 16'-20' TT or tents. Commercial RV parks are usually crowded with smaller sites because of the land cost. The more spaces in a park = more income.

As a first time buyer, you would probably be more comfortable towing a shorter unit for awhile.