I still had an "F" on my license(but my name had been changed) when I applied for my current job. I wasn't filling out online forms, but I did end up ticking "M" on the paper application and didn't run into any issues with him. It may make more sense to potential employers if everything "matches up", you know? I used a teacher for a reference, but I don't quite know who else you can use other than your former employers.
You don't have to explain your transition to them, but you could contact the ones you might prefer to use as a reference and say "I am going by *name* now, just a heads up", if they didn't know you by that name when you worked for them.
Let's see...Any other tips...
Don't feel like you have to explain your transition to anyone. What you do for your health is none of your potential employers' business.
Try and be as flexible as possible, people are more likely to hire someone who doesn't dictate their hours to their boss. Of course, if you need to ask for a certain day off to do your business and such, I think that's acceptable. Everyone needs that.
If you have any concerns, ask about them! Write things down, especially because it'll help you remember them for when you have an opportunity to talk about them. I like to take notes when I job hunt, because it's good for future reference.
Make sure you can communicate well with your potential employers, too. It should be easy to talk to your boss, you know? Not like pulling teeth from a shark. :p
Good luck!