You can use whatever name you want, it's YOUR file :) .log extension aims to communicate that a file contains logs data instead of simple, general text as .txt would suggest, but if you feel more comfortable with .txt (probably because it's better to double-clik in some file exploring facility) go ahead.

For the emailing part, you can peruse Q&A about it for some hints; I personally use Jenda's Mail::Sender to send emails with attachments and find that it serves excellently to the job.