Checkerplate is PITA but not terribly hard with something like 3M180, some heat and a good roller...
It might tent a bit later on but if you do a line of adhesion promoter around the outside and roll it in fairly warm it should stay ok...
I typically tell the customer the deal and let them decide...sometimes that bar can be worked into the design but sometimes they just end up with this trailer second hand and have a different thing going on already...
We have done the screws both ways...usually fairly big and a pain in the thumb to sink over but its also pain in the ass to remove the vinyl later if you remove screws to install...sometimes putting the screws back can twist the vinyl or you can break/strip screws...If its a long term non brand specific trailer decoration or horse trailer I might bother to remove the screws but if its a commercial wrap with logos/lettering/etc that might change with the wind, I would go over the screws and make it easier on future you if this is a long term customer...its kinda nice to install with no screws but then you have a bunch of screws in your design...