1) As everyone else has said, minis are not required. C&C is really patterned after 1E, so they are no more required for C&C than they were for 1E.
2) The PHB is all you need. As a DM, you might be tempted to buy the Castle Keeper's Guide, but don't. It's not like the 1E DMG which contained rule clarifications and more information. It's a useful book, don't get me wrong, but unless you're running a campaign, the PHB is all you need to play and run it.
As for monsters, they do have two good books (Classic Monsters and Monsters and Treasure; I'd stay away from M&T of Airdhe, at least for monsters), but as others have commented you can use anything from Basic D&D through 3E. I ran White Plume Mountains without any pre-work to convert, just doing the AC and attack conversions in my head, but I'd be careful about doing that with other editions. The C&C characters seem about in line with their 1E equivalents, so while you could use 3E adventures or monsters, you'd probably have to scale things back a bit to match the power level. I haven't done this, but others may be able to speak to this.
3) DM prep time is definitely much less than 3/3.5E. Even if you were going to fully stat out an NPC (something I never did in either system anyway, I'm a strong believer in improvising), C&C classes are much simpler, especially since there are no feats.
