To be honest, you shouldn't really be considering an animal simply because your girlfriend said thats what you can have.
If you don't have an interest, proper knowledge or be 100% sure you can always correctly care for the animal, it is better not to get it at all.

Not trying to put you off getting a reptile, but i wouldn't really consider either of these species good starter reps, and it would be aweful if you got an egg eater and then realised you couldn't find the right sized fresh eggs for it on a regular basis, or bought an anole and then got bored of it because you couldn't take it out and handle it.

I take it the issue here is feeding mice and live insects?
I can understand her not wanting crickets around the house, nasty smelly things, heheh.
In which case Blue Tongued Skinks may be a species for you to consider as they are good starter reptiles, not too demanding, become dog tame with regular handling from a young age and the meat portion of their diet can be cooked chicken or a low fat, high meat content cat food.

At the end of the day, it's going to be your new pet, and you are the one whos going to have to care for it, so really i'm just warning against making a decision that is right for your girlfriend, but not for you or indeed the animal.

Good luck with what ever you decide!