The name by which you're known professionally should be in it
"Professional" means not making people learn a separate nickname for someone they've never met. If you're known professionally by a nickname, fine, use it in an email address:
dr.dre@. The point is that when people see the email address they should associate it with you. It makes it easier for them to see that what they're doing is correct when they send messages. It's easier to hold in memory if it's the only name they know for you. Probably other benefits.
Nothing that you don't actively want to tell them should be in it
If it's an unusual domain name, a few people will look it up. So don't use
firstname.lastname@ your anonymous politics blog, unless you want to in effect introduce yourself to business contacts as "the author of this anonymous politics blog". It doesn't mean you're ashamed of it that you're not introducing yourself that way, it's just not your profession. If you're applying for jobs as a politics journalist disregard that part.
If you can avoid disambiguating junk, do so
email@example.com just is better than
firstname.lastname@example.org. It looks "neater", and neatness is a professional quality. Each little thing doesn't matter, but together they add up to a kind of "hygiene" that signals you've put effort into the details.
A secondary reason, you would be amazed how many people don't use copy and paste. Most people over the age of 30 have, at the critical point in their life when they bought a mobile, lost the ability to remember a 7 digit number for 20 seconds. Those under 30 never had it ;-) As a courtesy to others, do not make your email address hard to type. I won't go so far as to say that if your name is hard to type you should find ways to simplify it, but I slightly wonder if it would help.
Sure, it's hard to get hold of a neat email address at a major provider these days. It's also hard to write a good resume, so you can always try a few variants on your name while you're mulling that over. If you must add junk, try to think of some relevant junk. If your name is so depressingly common that you really can't get a decent
@provider address, maybe register a domain and throw up a few pages related to your profession. It doesn't need a whole lot on it, just your resume and anything you'd like a business contact to see. Finding a good domain name isn't all that easy either, but at least you're limited by your creativity, not your given name.
If you actually use it, it should remain the same for years or decades
This applies to any email address used as a general point of contact, professional or otherwise. You do not want to be that idiot who keeps sending out messages to your entire contact list with your new address.
You don't have to actually use it
Check the address on your resume for at least as long as you care to receive inquiries about that version of your resume. Or, you know, there is such a thing as email forwarding. Make sure that you receive the email, that you receive any error messages generated by email you send, and that you remember to send using the "correct" email address. Beyond that you don't have to log in to whatever awful web interface the provider has produced.
If you come up with a better email address later, you can put it on the next version of your resume and forward the email from the old one just in case. And even that might be overkill - I guess it depends what industry you work in, but think about your odds of ever getting a decent job lead from a resume more than a year or two old. Firstly you'll send an updated resume to recruiters you care about more frequently than that, and secondly who head-hunts with no idea what you've been doing for the last two years? My experience is that recruiters stop bothering you after about 18 months or three rude emails telling them you have a job/alternative recruiter you're very happy with.
Once employers hire you, they won't use it
They'll give you a company email address. So your resume address is solely about the hiring process. It's not even about maintaining contacts after you leave, you can give them any other email address you like. It doesn't need to relate to any of your other online activity unless you want it to as part of what prospective employers will see if they choose to research you. Between lack of time and consistency in hiring procedures, many won't, but some will.
If you plan to change jobs a lot, things are a bit different
If you're perpetually looking for work (for example as a contractor) then you do want a single permanent email address for the purpose. It's probably best to register a domain in this case. Depending on the jurisdiction you're in, you might want a specific name to trade under anyway, even if you don't have a registered company. This doesn't need to be your own name, and
email@example.com is ideal. Or your national equivalent of
.co.uk in my case.