Tetsucabra armor is a good starting armor set. Take a look at the G Jaggi and Velocidrome armor as well and see what you like the most.
For getting any monster again (not just G Jaggi), yes, you can just do the quest again, or alternatively once you beat him in the campaign, go to the expedition area and do a couple of expeditions and see if you can get a guild quest pop up with the G Jaggi in it. Note that the guild quest you can get from an expedition is not always the same monsters as the one in the expedition itself. Once you get one, register it from the Guild Quest list in the menu, and go into the gathering hall and you can replay it multiple times. Each time you do, you level up the quest so it does become a bit harder, but on the plus side you also can get more rare items when it becomes rare (it will tell you when).
A common problem to have is that if you have good weapons and go to fight an early monster, such as the G Jaggi you may kill it before you break all of its parts (such as getting the King's Frill). You could then go into the Gathering Hall and solo the G Jaggi quest in there, as it has higher health than the one in the campaign as the monsters in there are balanced for 2.5 players.