TLDR
Will core cards (i.e. Counterspell) remain in rotation, if so from what set?
What rotation do intro packs come from?
Cheapest+funnest way to get into the hobby?/If it's even possible, what's the cheapest way to build a mildly competitive collection for Standard?
Any tips from parents getting kids into the hobby?
Thanks a bunch everyone!
1.)No, there will be no more core sets. Magic Origins will rotate out of standard when Dragons of Tarkir does, about a year from now. There will always be a few reprints in each expansion, and any older copies of those cards you have will be legal as long as that expansion is legal.
2.)Intro packs will have cards from all sets in the block. Dragons of Tarkir intro packs include cards from Fate Reforged, for example. This is going to be confusing for a year, as Khans-Fate-Dragons are a "block", but for the purpose of standard rotation, Khans-Fates is a block, and Dragons-Origins are a block. This means that if you buy a Dragons of Tarkir Intro pack, it will not be legal when the Spring 2016 large set comes out, and standard rotates.
3.)Your TLDR question is pretty different from the longer question you asked, so I will give 2 answers. If you just want to get into the hobby, buy a Deckbuilders Toolkit or 2, and some of the ancillary products built around what you are interested in (ie, Commander decks if you want to play Commander/EDH, Duel Decks if you just want some quick jump-in experiences). If you want to show up at a Standard FNM and not be completely embarrassed, buy 2 (or more) copies of the most recent Event Deck or Clash Pack, and combine all the cards into 1 deck. For anything more than that (lets say you want to consistently be near the top of an FNM, or play in a GP or Open), you should just be buying singles, as it's significantly cheaper than just buying boosters.
4.) Not a parent, but all I would say is that if he doesn't seem to take to it, it's best to drop it and maybe try again a year or 2 later. Don't force it on to him.