Overall, he should try simple champs as much as possible. I can't recommend specific champs because what might work for me may not for him.
For jungler, I really don't recommend just maining one champ. I really feel like you need to have a range of champs that can work with your team's comp or can fill a hole. So he'll need an initiator, someone who can wave clear, an assassin, a hard carry, a split pusher, a tank, someone with CC, a physical focused damage champ, a magic damage focused champ, and someone you can safely first pick without knowing what your team will pick and isn't hard countered. Of all those things wave clear, crowd control, and initiation should take priority as roles to fill. As long as your team has all 3, you should be in good shape.
Yes you can one trick as a jungler and it'll get you out of bronze; you can one trick weird crap up to mid diamond. However if you really want to git gud as a jungler, you have a lot of work cut out for you.
As for top lane, just learn about minion and wave control. IDC who he picks, if he learns those things he'll get out of bronze faster. He then should learn about match ups and have a champ or two he can play in reserve in case he needs to. Top lane IIRC is one of the more match-up dependent lanes in the game.
Once he picks his champs he needs to learn what they do and when they have power spikes and when they have power weaknesses.