- Use your real name
- Use a company name
- Use your existing domain name
- Don't look like a massive spammer
- Don't act like it's a Hotmail account from the year 2000 (x_hotStuff86_x)
- Don't brag like an idiot (PUAmaster... oh wow, that exists. On second thoughts, not surprised.)
- Don't use the same username you've been using on forums and game sites for the past 10 years. Remember that one quick google search may reveal more than you wanted to share.
- Don't use easily forgettable keyboard mash. You're not Randall Munroe so unless you have a site as clever as xkcd, all you're going to do is get yourself forgotten.
Given that Twitter does not work like an e-mail provider, where you can just select a different service if you can't find an alias you like, it is slightly reminiscent of those early Hotmail days where everyone scrambled for a decent name and then ended up resorting to birth years and numbers to distinguish themselves.
Overall, unless you were an early adopter, you're likely to find that all the best names are taken and the number of reasonable available combinations for the 15 character limit is pretty small. Still, keep trying eh?