I liked the 5e Starter kit and the Essentials kit. They limited the array of options to the basic essentials, and explained clearly how things worked, all in a small magazine sized pamphlet. No Idea about the new one- I don't own it.
I am also an old grognard-ish. I do enjoy a lot of the ideas in modern D&D- the mechanics anyhow. And it's very difficult to go back to the old ways of few options, glass jaws, and a different rule system for everything. (compare the gold 1e character sheet to a modern one) IMO, the best part of the 5e boxed sets is that you don't have to wade thru paragraph after paragraph of High Gygaxian to get the one nugget of info you needed, like we did lol. (well, why the hell didn't you just SAY that, Gary???)
If you can find one on Ebay, grab it.
I actually liked the pregen characters in the Basic kit. Again, they clearly explained all the stuff. Even gave them some background, personality and all. Not a bad idea for a one shot, or short mini campaign. Then let them roll one up on their own, if they get the bug and want to continue. And, for Pete's sake, don't be a Richard and make them roll 3d6 down the line- you get what you get... You want them to LIKE the game, right?
you might even dig through the ridiculous collection of adventures, Dungeon mags, and home brew adventures we all seem to amass, for beginning adventures. Converting is pretty easy- if you don't sweat piddling stuff like I do... A Fun, interesting time is WAY ,more important than strict adherance to RAW or the official approved way of the day. Even better, if you refuse to obsess over balance. I just swap monsters with the (whatever edition I'm running) version. Same for spells, and magic. 5e characters are fairly sturdy, compared to the one punch chumps we started with- and you can always TALK or retreat. Point that out if needed.