I'm about to start this DLC for the first time, and I was wondering whether or not you start with your inventory. If not, just say no. If you do start with your inventory, is there any recommendations of what I should go in with? My character doesn't really have all that much right now.

Yes, you do. Take whatever you're good with. But so you know it does say 15+ for a reason, there's a lot of high skill/S.P.E.C.I.A.L. checks.
For the most part you're handed all you need for the DLC.

I'd bring a fair bit of stuff, I went in very light the first time and ran out of both ammo and health items without melee and one of the new perks I would have been screwed. Ammo for guns and explosives is pretty minimal and the store carries only a few rounds thats the biggest issue with OWB in both DM and HH equipment and ammo were plentiful in OWB theres a few hidden caches but not enough to get you through on the higher levels.

Yes you do, same with Lonesome Road.

Take everything you have, it's worth it because you first arrive at the best player home in the game. Though I actually suggest to take as little as possible (assuming you are on Core like me) because if you come with your full arsenal, then why use the K9000 if you have the Anti-Materiel Rifle? Or the LAER if you have the Alien Blaster? Well, those are my thoughts anyway, you may have a different experience then I do.

I'd suggest you stockpile on as much ammo as you can for your best two guns, you'll probably end up needing it if your anything like most people on here.

Thanks guys.

Yes, take lots of ammo. Twice as much as you think you could possibly use up.