for new construction or remodeling or just best safety all receptacles outdoors, garage, basement, bathroom, within 6 feet of a sink (like kitchen) should be GFI.
so putting a GFI in your basement at the start of the circuit is a good thing. the GFI is 1.5 inches deep so you need a 2.5 inch deep box at least, with no conduit closer than 1.5 inches to the front. if you need a deeper box the basement is generally an easier place to place or replace one.
fuses and breakers are for fire protection and not so great for people protection. as engineer_comp_geek mentioned GFI devices protect people.