The biggest thing is whether you like her - could you spend 24 hours in a room with her. Also, does her birth philosophy chime with yours. Some doulas are focused on a particular discipline (homeopathy, for example, or hypnotherapy), and if that's not your thing, they won't be right for you.
I'd also look for someone who is experienced and positive about dealing with birth trauma and planned sections. She might help you decide to go for a VB, but you equally want her to be good at preparing you for the section, since it's unlikely she'll be allowed into theatre (unless your DH/DP doesn't want to).
There's a great list of questions somewhere with more practical stuff and I cant find it. Sure someone will link soon. Stuff like how she charges, when you can contact her and what happens if she's not available (e.g gone down with food poisoning!).
My doula was SquiggleyWiggler, who is on here (we've both mentioned it on a few threads, so I don't think I'm compromising any anonymity!). If she's about, she might know the list of questions I'm on about. In all honesty, I ended up just having a chat and she automatically went through all the practical stuff.
Oh, and finally, I had a hideous forceps birth for DD1, and had DD2 at home in the pool not long ago. An elective may well be the right decision for you (I was not phobic, and really wanted a better VB this time), but I'm just sharing that as a positive story for what it's worth!