One very important "rule" for new research is to start where you are, go slow, and document as you go. That means you will have acquired birth certificates proving your father, and his father.

[Vernon Sizemore had multiple children but I can only find records of one, Vernon Dorsey Sizemore(born 1929 in Georgia)] People are mentioning "vital records" but these are not available in GA until after 1919. Your grandfather should have a birth certificate, being born in 1929. Also he and his parents should appear on the 1930 census. In April, after the 1940 census is released, you may be able to identify his siblings.

You need to find your great-grandparents in the 1930, 1920, 1910, and 1900 before going back further. Then you can check local records for their marriages, or obituaries or cemeteries. One resource I find helpful online for local records is the state versions of USGENWEB. If you go to the main site, you can go to the state you want, then to the county you want. They work from volunteers, however, so sometimes you find a lot, and sometimes nothing. It's always worth a try. If you make the connections via census records, any of them who lived past 1919, you can try to find a death certificate - sometimes they have their parents names on those, if anybody can still remember who they were. That might establish your gr-gr-grandparents.

Please do not believe all the hype that any of these for-fee sites tell you about what you can find on them. I don't care what that site said it has, the guy who ran a search for you is telling you the truth. You will be very fortunate if you find what you need that way. If I can get a death date from a tombstone, I can usually find an obituary in our library's reels of old local papers. It's worth the effort. Nobody is being rude by saying that there are very serious limits to what you will be able to do online. Although more records become available everyday, little rural communities are rarely high priorities for anyone to post online.

If from the census you determine that they owned land, rather than just renting, you might be able to find probate records that establish the relationships.

Genealogy is not a pursuit in which to expect quick gratification. I've worked on my family since 1972. Some lines are back 10+ generations, and some I'm still stuck on my great-grandparents. These are families in GA, TN and NC. Some of my best finds have come through developing friendly & courteous relationships with other researchers.
Good luck in your research.