Glue guns, I have found, are difficult to work with for this application...having used them for otherpurposes, I woul dnot choose them for grill cloth.
I use Titebond for Mouldings ...available in most hardware stores, is quite thick so it does not run and set up quickly.
I use "Acco" type clamps (black metal clips for bundles of documents or stationery ... availabe in staionery or 'dollar' stores and come in various sizes.
Nothing wrong with staples if it is a power stapler but if manual, a lot of work!
Good luck!