If you want to check out Ancestry.com for free, without possible hassle of getting them to cancel your "free" 14 day trial, go to your local Family History Center.They are online and have a subscription to Ancestry.Plus, volunteers will show you how to use that site, too.
You'veprobably used the FamilySearch site (LDS).On their new main page, near the bottom, you can find FHC nearest you.
Pedigree Resource File index information is on FamiySearch.Your local FHC should have the CDs with the full information submitted.Again their volunteers will show you how to use the Ped Res File CDs.
Also, check public libraries in your area.Only libraries can subscribe to Heritage Quest.If your public library has that subscription you just need a library card with barcode and password or PIN, and you can use that online at home.HQ has many of the federal censuses indexed, PERSI, Rev Soldier pension records and over 25,000 publications indexed (you can only guess how many names that would mean.)
Be sure to check out GenWeb sites.They are manned by volunteers, so they do vary in amount of material posted.Most people use the county sites, but don't forget to check out the state levels, too.TX and TN are among those with some good stuff at the state site.
This will take you to the U.S. level, from there you can choose any state, and once at the state level, then choose your county.
Have you found a genealogical society near you?Often they offer classes to help people getting started with family research.
As for the site you mentioned that said you had to do research by mail.I think you're referring to the Soc Sec site.You are not doing research, you are paying for a copy of the application filled out to obtain a Soc Sec card.Person filling out that information should know the names of their own parents etc.Also, it will show residence at time of application, too.