There are just a lot of things that bug me about this - could end up being a CL hall of fame post in the near future. And I'm not trying to antagonize - just point a few things out.
1. Why are you auditioning a person that you don't know what you're going to do with them? Typically bands have a need for something and go shopping.
2. "Ideally both guitarists would be able to go back and forth between rhythm and lead." Is your current guitar player on board with this? In most bands, one guitar is primarily the "lead guy" and the other is the rhythm player. some lead guys are fine with sharing duties, others are pretty protective of their spotlight. Some bands will alternate who plays leads, some don't. However it works out, you need to know exactly what your new person will do and let them know exactly what that is so they can make good choices for them selves and to allow them to prepare accordingly. Lots and lots of guys can throw decent rhythm support, not so many can do leads. You need to have a specific role in mind before advertising.
3. Once you define the role, you can determine how to audition. You should use songs that are, or at least could be, in your playlist. get what @LBS-bass was going for, but do you guys really want to learn songs just to audition folks? You don't need a lot of songs, (4-5) but pick songs that will demonstrate their ability to do what you need from them. If they will be doing lead and rhythm, make sure they demonstrate both and make sure they KNOW what their role is on each song. And make sure you guys know the songs well - nothing more embarrassing than when the auditioner knows your songs better then you.
Again, not trying to give you grief, but it doesn't sound like you're ready to even post for an audition. Best of luck.
And, BTW, I can't help you with specific song suggestions as I doubt I could even name one song in that genre