[RICK LAKE]

Ebruce. Unless this is a arp bolt with fancy end on it, You have a choice.
I have used both. Home depot or Lowes carry long bolts in grade 5 which is good for you. Since we don't know why the old one came lose, here a way to fix it.
You didn't say if there where any spacers behind the alt and between head. You are going to need to check to see if the belt is straight on all pulleys. I have found a piece of string or bunge cord both work well to center belts on pulleys.
With a threaded stud length, you install it to give 3-5 threads with the nut tight and cut off the extra. Loc-tite stud into head with blue or red and reassembly part. Also get a nyloc nut for this. (Air craft nut to keep on and tight)
With long threaded bolt, you want about 7-10 threads into the head and leave 3-4 extra and not bottom out stud in hole for tightening. Also red or blue loc-tite. If bolt is too long, cut off threads until get right length. Habor freight sell a $10.00 caliper for measuring depth of holes in motors and heads. Get one for easier repairing of this problem.
After road test, if bolted into head check for it being tight. If no movement, don't tighten. Problem with loc-tite is one install only and no adjusting after. If you are looking for a torque setting, about 35ft pounds on aluminum heads and 40ft. pounds on iron ones.
Side note, if you have the room, adding a 3rd bracket to the alt would help support the alt and stop any vibrations fron the motor or belt. Small piece of steel strap 1" wide, grind the edges, drill 2 holes, bend the ends in a vice, paint and install will help down the road. Some Alt have a bolt hole in the back of the unit for additional brackets. Use another hole in the head of a front intake manifold mount bolt. There may be a kit for this already on the market. Try Summit or Jegs. Good luck. Ps you will need to get the correct thread pitch and sae or metric. Guessing 3/8" or 8mm for size. Coarse thread. Match up the hole with old bolt.