I would suggest doing more than 1-on-1 battles (well once you get past the "this is how you move, and this is the turn sequence part), and hey if he's just getting the new box, let him use the mechs in there (if he's anything like most big kids who like playing games, he's gonna want to play with his new toys).
1-on-1 becomes an initiative luck-of-the-dice game with fairly equally capable mechs, and a single horrible crit could make for a very short game. lance versus lance is great to see that despite some bad breaks and some lucky breaks, the game goes on down to the last mech hopping around using its own arm as a club after all its guns have been shot out. lance-vs-lance lets him learn the trickery involved in prioritizing initiative with your moves, which in my opinion is one of the most important things to become a good player instead of just someone who knows how to play.
I ran a few games last fall using 1 intro box set and 6 players. I played against each one individually with the same lances that I felt were a good spread of all the different play styles, then let them draft their mechs from the 24 available (we didnt use the clan stuff) and each have their personal lance to duke it out with each other. There are many possible combos, but I chose these:
new player's lance:
spider: (teach the power of J7 into cover, backstabbing, baiting bad shots, and a bit of heat discipline)
trebuchet: (range bracket specialist, good for how to play to the weaknesses of the other guys weapon ranges to your advantage - also good to teach how to conserve ammo and be sparing with those LRM salvos until you have a good shot)
grasshopper: (its durable, but not very hard hitting so it wont demolish smaller mechs in one volley on a bad move. just something that could use its survivability to show that even popgun weapons add up as a game drags out... aslo, it is a contrast to the other mechs because it is so heat efficient, let them appreciate how valuable that can be instead of just having more guns and armor)
atlas: (because its huge, hard to bring down, but they learn the limitations of movement and weapons range. Let them have the AC/20 and show them how it isn't necessarily the awesomest gun on the board if they can only seldom close with it)
--- versus
teachers lance:
commando: use it to lurk, make them aware to think a turn ahead when they move or get slammed with a hit and run guy if they find themselves in the wrong place
enforcer: teach them to fear the big guns how not to be victimized by them, and why it is good to identify the biggest threat and concentrate fire on it. It''s not hard to bring down, but it punches some nasty holes if it isn't dealt with quickly.
quickdraw: because its quirky. the plan was to bait the initiative, its size and jumpiness make it ready to exploit poor positioning, but its light armament means it wont be too harsh a lesson.
zeus: similar reasons as the atlas, it takes a while to bring it down. Its not as terrifying as the atlas closing in on you, but it's very mediocre and gives them something to shoot at for a while. little rear mounted laser on this and the quickdraw gives the spider backstab tactic something to think about. Also this was just a quirk of mine, I wanted it themed just for a sense of fluff continuity so its staying with a kind of fed-com theme)
---so this wasnt so much to learn the specifics of the mech being used, but to learn the kinds of things to think about in a game, so many different approaches and considerations going on at once between initiative, range bracketing, backstabbing, bubble-of-death type mechs, ammo conservation, heat management --- and all right there in his box.