Most of my addresses come from Star Tiger which is a paid for site but is only around £6 per month. A similar free site is fanamil.biz. However, both of these sites are more entertainment than sports focused.
You can also get a lot of information from a simple google search, searching for the persons agent or representative etc.
Regarding football, I too am a Liverpool fan and have a quite a few replies over the years, although its not my main area of focus. A lot of ex players may still have links to a club in an ambassador role or similar and others may own business so could be contacted that way. Home address are a little harder to come by and aren't really my area of expertise. You could also try contacting people through social media or even their own websites
There are many Liverpool forums on Facebook who hold private singings with lots of ex players but obviously these cost a bit more than he price of a TTM request
Research is key, if you are going to send out potentially valuable ticket stubs then I would only send them to address that have had recent replies. The golden rule of TTM is never to send anything that you would hate not to get back (although sometimes the gamble can pay off).
always write a polite and courteous personal letter and include a SSAE
Good luck