The career agent missions can only be run once. If your character already did them, they can’t be done again.
You can roll up a new Alt if you really wanted to redo those starting career missions, or you could just do regular missions if that’s your thing.
So, there’s actually two places you can find career agents. In the career agents section of the agency, it will only show you the default career agents for your race/background. However, if you go to the agent finder in the agency, and then filter for career agents, it will show you all of them. What’s more, it will put a red “x” (or something like that) next to the agents you’ve already run. Thus, you can easily who’ve you ran, and who can still run.
And, just to reiterate what others have said:
You can only run each set of career agents once, but you can run all 12 sets.
Yes, they do give you a nice boost to faction standing, as you can blitz an entire set in about 2 hours.
Recommended ship: t1 kiting destroyer with a good align and hyperspatial rigs fit. You don’t need any tank, and don’t need to do a whole lot of damage (168dps rail gun catalyst one shots a majority of stuff). You will have to do some burning, but not an excessive amount. Thus, an AB is fine.
Recommended order: Exploration → Both combat agents at the same time → Both Industry/trade agents at the same time
And, if you’re going to run more than one set, you might as well and scan down and get 11 copies (or however many you need) of the proof of discovery documents, all in one go (you will need the gas passkey to get into gas site, which is given when you accept exploration mission 5). This will allow you to complete exploration missions 3-5 for the other agents without even undocking.
You don’t have to worry about bringing anything else, as all the required items will be rewards from other missions, or easily purchasable from the station’s market at a very cheap markup for vets (well, aside from the civilian shuttle that you need to build, but that literally takes 5 minutes, and the trit for it will be easily procured).
Shouldn’t need them reset. Just find a group you haven’t already completed. I doubt you’ve gone and completed all three careers agents for each career, for each faction - that’s 12 versions of the same career path.