Speaking as a manager who's worked with MtF transgendered folks in the US, but not actually managed to hire one...
1 - Looking at a resume
I look at resumes incredibly quickly. I care about the name because I want to know who I'm going to be talking to - what name they want to be called in the interview is key. So I want the top of the resume to accurately reflect who I should ask for when I call or walk into the interview... I want the question "Are you Jane?" to be greeted with a "yes", not an "I used to be" - so I'd say go with the female name to avoid confusion, if you will be living as a woman.
2 - Reading deeper
I will (hopefully) read beyond just your name, before making a whether or not to interview decision. For any gender neutral affiliations and jobs (for example, a engineering certification which is likely to be earnable based on ability to past a test, not on gender) - go ahead and claim it as woman. As far as I'm concerned, you earned these things because you are smart and worked hard, and not because of your gender.
The trick would be for any exclusively male jobs or affiliations - if you are a Mason, or a Male Figure Model featured in Gentleman's Monthly - I would suggest leaving these things off as part of your past life. My reasoning:
If this is a job you absolutely must be a male to do (male figure model) - then you are no longer qualified if you are living your life as a woman.
If this is an affiliation granted exclusively to men, and not overly relevant to your job, you can afford to leave it off. For a case like the Masons, I realize that it's nice, and somewhat useful, to be able to show the affiliation - they are after all a volunteer group that can be well-organized and able to create a profound impact for good, which is nice to show on a resume. If you feel very deeply about the work, or feel a major facet of you is left behind by omitting, then go vague - "was a Mason" = "formerly part of a multinational nonprofit focused on XYZ".
3 - Reference Checks
Understandably, if you have degrees and former jobs, you have the problem that the name of the person who got those credentials and your current name are different. At least in the US, "references available upon request" will cover that initial submission in most cases.
If references are asked for up front in the process, list the way to refer you as a complete thing - "Degree from XYZ, Major ABC, for verification call phone number. Degree attained under the name first, last, which was later changed". You may want to provide a reference to the paperwork for your legal name change when it happens.
The goal is to streamline expectations and to give as consistent a picture of who you are now as possible. Knowing who will be walking in for the interview and what they are capable of/qualified for is the ultimate goal. The process of who to verify who you are and that you've done what you said you would, is secondary.
Also - one thing women do frequently is reference maiden names. We often use "nee MaidenName" or "formerly ThisFullName" - and I think you could likewise.
Will it totally obscure that you are going through a transition? No. In all honesty, having had a number of friends and coworkers make this journey, my general conclusion is that the first year of it is pretty hard and awkward for anyone going through it, so be ready to embrace the awkwardness and have patience with yourself and others.