Have you DMed before?
Yes, but only twice, and we did not finish either campaign. The first time was a version of Curse of the Crimson Throne that went off to do its own thing somewhere in book two, but still fun.
The second was a campaign for newbie PF players with one of my current fellow player as a helpmeet to help us all out with the rules. It was great fun because it allowed me to grow along with my players.
If not I highly recommend starting with a published adventure. It doesn't have to be a full adventure path or heck even pathfinder. But it should be pathfinder compatible. Prep the adventure (reading it, understanding the tactics the monsters will use, etc.) and run it as is and don't worry about the PCs breezing through it. The point of the adventure isn't so much to challenge them but rather to get a feel for what characters are capable of.
You should also be comfortable adjusting things on the fly if an encounter is too hard or too easy. If any players are using optimized characters you should probably go ahead and set all the enemies HP to max. Sometimes I'll even give my monster's one final gasp if it feels like they went down too easily.
For example, my monster has 5 hitpoints left and the PC just nailed them for 30 damage. It's only round two and he's the BBEG and it would kind of suck for everyone if he went down already. So instead, the attack leaves him at 1 hitpoint. If any other PC lands a blow and does any kind of damage he's dead, but the players don't know that. It creates tension because they just threw everything they had at him and he's somehow still up. Now my monster gets to potentially do one more thing before he drops. Even if he doesn't, he's probably getting dropped by a less optimized character. Everyone feels like they contributed and the fight is more satisfying for everyone.
I do try to keep these kind of shenanigans to a minimum though so the players don't catch on that it's what I'm doing.
Even if you've DMed lots of games, published adventures can still be useful. They take less effort to prepare, which gives you more time on the custom stuff. If players are blowing though things too fast then plan adventures based on a higher level. You might find that maybe your group is only really properly challenged when they are up against things that are for 3 levels higher then their actual level. Though in this case you may need to reduce the xp...
Also thanks for those suggestions - I have a few APs I could run if the players feel like it, and I'll definitely read through the ones I have for ideas on how to build enjoyable encounters in what I hope is already an enjoyable story.
Thanks for the advice and examples.