Be true to life
Many Xbox Live users have been online for quite some time and use the name they are best known as, which is often their e-mail address. There is a small risk of spamming if you use your e-mail name as your gamertag, but it will easily identify you to friends and family and make you easy to search for, as well as easy to remember. Do not, under any circumstances, however, use the same password for your e-mail and your Xbox Live account.
Use your identity
If you already have a recognized personna in any online community, especially one relating to gaming, make an effort to retain it. Even if you only use part of your recognized handle from, say, IGN, or if you have to add a letter or digit to your handle, it will make you more easily recognized by friends than if you start from scratch. The simplest solution, if your usual handle is taken, is to add Xbox to the beginning or the end of it, keeping your identity straightforward and easy to find.
Dos and don'ts
Xbox Live employs full time censors to make sure people do not use gamertags that are considered unacceptable or offensive. You will not be permitted to create a gamertag that is considered offensive by the Xbox Live screening system, and your account can be suspended at any time if your gamertag is determined to be inappropriate. Do not use any words that could be considered offensive in your gamertag, even with alternate spellings or digits replacing letters. Do not reference politics, religion, or race. Do reference Internet memes other players will recognize and appreciate. Do switch out letters for digits in unoffensive gamertags. Definitely make the effort to stand out from the pack and make yourself more memorable.