I haven't fully settled yet, but I arrived at my top choice with the criteria:
1. Definitely female (Ironically, my current name is more female than male).
2. Ordinary - there's a lot of pretty names out there that I like, but I'd rather not stand out.
3. Same initial as now - not essential, but it felt right.
Slightly annoyingly, this is the name I 'jokingly' used when I cross-dressed a couple of times at uni, chosen then purely because it was broadly similar to my name. Those aren't great memories for me, but it was years ago and I'm unlikely to cross paths with any of the people again, so I'm trying not to let that get in the way.
It hasn't been mentioned, but many people choose to change surnames too.
I will, partly because I just don't like mine. Even before making the gender decision, I was planning on changing my full name, and I would love to right now, but I think it would be a bad idea to change now, then in a couple of years as well.
As far as reasoning for surnames goes, I was considering taking my mother's, in a strange 'rejection of the patriarchy' type feeling. But I felt that'd seem negative towards my father, who I do not dislike personally (he's fine with me ditching his surname; even he doesn't like it). I feel that a completely whole-cloth name is equitable for everyone.
Surnames are also a great place to choose a name with a meaning, even more than first names - most names have meanings, albeit often obscured by language and time*, but that's not often important. Surnames can be much closer to actual words, while still being fairly unremarkable.
* My birth name was chosen as being from my father's birthplace. I've just discovered that's the origin for my chosen name too, though completely unrelated!
