I was originally going to get a case, but after using the one Apple included...I won't be getting one. It suits its job just fine...protects the iPod and when used in conjunction with the remote, works great
My first accessory was new headphones. The ones that came with my iPod just didn't fit/feel right in my ear. I ended up getting Sony MDR-EX70's and I'm very happy with them. They very good at blocking out the noise on my train rides and feel good in my ear.
Depends on the person. I have some new sony headphones, but I lost them somewhere in my house. If you clip the tag in the included case, it works very well (especially if you have something like the iTrip).
Hmmm... there's the tradeoff. I've never listened to the Sennheisser series, but I would hazard a guess here: If you are listening in loud environments, go for the EX70s, otherwise the Sennheissers would offer better sound quality.
Definately the first accessory to get would be a case. I have only had my new iPod for one day, and have even kept it in the plastic it came in, and the entire front is covered in tiny scratches. I have no idea how they got there; iPods are scratch magnets. Seriously, that is the first thing you need to worry about if you like keeping it new looking.