One antenna to cover VHF High to 1300? That pretty much leaves you in the discone market. Which one you chose depends on your budget. Diamond DJ-130 with the N connector is a decent hobby grade antenna. At the upper end of the antennas designed coverage, you really want the N connectors. Resist the urge to go UHF connector….
Grounding needs to be done in a number of places.
Commercially, the coax jacket would be bonded to the tower leg near the top and bottom of your tower. Reputable coax companies make grounding kits for this. Usually at the bottom of the tower a ground buss would be installed to connect all your coax shields to the ground point under the tower.
You then need to have an entrance protector where the coax enters your home. That needs to be grounded.
And all your grounds need to be bonded to the homes electrical ground rod, in compliance with the National Electric Code.