I second Lord Xaviar's recommendation for Sinister Secret of Saltmarsh. It's levels 1-3, runs fairly easily, and was rated one of the top 30 modules of all time. It also includes pre-rolled characters inside (I think) if you wanted to just pick it up and start playing.
His other recommendation of T1 Village of Homlet (or the expanded T1-4 Temple of Elemental Evil) is also solid. If you go T1-4 you are heading off onto a level 1-10ish campaign path, so it kind of depends what you are interested in. if you are in it for the long haul, go ahead and jump on board with the full T1-4, but if you were looking for something shorter, then, again, Xavier's recommendation of just T1 is a good one.
Another SOLID 1ed module is Against the Cult of the Reptile God. It's levels 1-3, and I think it's actually an even better module than the other two, but it can be quite challenging for players and a bit deadly, so while I love it and recommend you looking it over anyways, if your players are all new then it might not be the best option.
Finally, Keep on the Borderlands is THE classic introductory module. I know that it was originally for the Basic set, and I don't know if it was updated for 1st Ed, but this is the module that myself and most of the D&D gamers I know cut their teeth on. It is well balanced, easy to run (for both players and DM) and has the flexibility to allow a new DM to easily either 1) strictly follow the module, or 2) Improv to add his own color - depending how much time/effort he/she wants to put into it. Either way would be successful and fun for the players. I always recommend Keep on the Borderlands as a good starter.
