I must say thank you for this lively discussion as after 20 years I'm attempting at getting back into D&D. My 2 boys always want to learn to play but at the moment I'm stuck as I started with the Red Box back in the 80's and progressed to AD&D from there. I have the 4E PH and was considering getting the new Red Box so that all 3 of us could learn the basics, but part of me just says go back to AD&D 1e.
Those are both reasonable choices, I enjoy both games. In fact I'm running a 1e AD&D game on Sunday using the OSRIC retro-clone, which you can get here for free:
OSRIC Download - then on Monday I'm playing in the 4e campaign!
If you want to try your hand at 4e, I think the Essentials products are much more accessible than the earlier releases. I'd recommend:
1. Heroes of the Fallen Lands - to create traditional Fighter/Cleric/Thief/Wizard PCs.
2. Monster Vault - for monsters. Includes great monster-tokens, a map, and an adventure too.
3. DM's Kit for DMing, though you could probably get by for awhile with just the Rules Compendium, it has the basics on encounter-building and you have your PHB for magic items.
In fact you could probably get for awhile by with just your PHB, Monster Vault, and the knowledge that encounters comprise the following monster XP totals:
Encounter Level
1 - 500 - eg 5 1st level goblins, 100 XP each
2 - 625 - eg 5 2nd level monsters, 125 XP each
3 - 750 - eg 5 lvl 3 monsters, 150 XP each
4 - 875 - eg 5 level 4 monsters, 175 XP each
5 - 1000 - eg 5 level 5 monsters, 200 XP each.
+4 levels = x2 XP.