I recently bought the classic module S4 and have read it over a few times. While, ideally, i'd love to run it for something like DCC or Worlds Without Number, I think 5e might be the easiest way to run it for now. I also have a few questions:

• Would there be any interest in the 'dungeon' part of this adventure, forgoing the 'hunt for the lost caverns' part?
• If the game limited classes and player options to what is in the PHB, would people be less inclined to play?
• If I made some modifications to the module so that even those who have played it before had new content, would people be more inclined to play?

And
--> How do I keep people interested after the initial few weeks after the start of the game? Any tips or hints?

There's always interest in a 5e game.

Eliminating what is about 2/3rds the character options will reduce interest, but it won't eliminate it.

Some folks like knowing what is coming, some don't, so that's probably a draw.

I have bad luck with dungeon crawls. They get repetitive after a bit: Check door, open door, kill things, search room, repeat. Good treasure and plenty of experience help alleviate this, but there's only so much you an pass out in one dungeon.

All that being said, I'd be interested, and I could limit myself to the PHB if I had to, but I'd rather not if I don't have to. I like some of the extra options and I haven't had  a chance to try them all out, yet.

I'd be interested if it were 1st or 2nd edition, not 5th. Good luck, happy gaming.

I've found it's best to decide what you want to run with the limitations you want to impose, then ask for interest. Otherwise you get dozens of answers, most of which will contradict each other, from dozens of people, most of whom won't actually be interested in the game regardless of what you decide. You'll also get people pushing back against any restrictions to official content, regardless of the hows or whys behind those restrictions.