I started hunting through Ancestry with a few guesses in mind:
- If Samuel was born about 1800 (I found 1801), he would probably have set up his own household and married between 17 and 30 years of age. So he should have his own census records starting from at least 1830.
- There are a few common spelling variants for Brierton: Bryerton, Briarton, Bryarton and I used those as alternative search criteria
- I searched for him but also for Mary Brierton and Mary Mann. Sometimes names on census records had the wife's maiden name and sometimes her married name.
I believe I did find Samuel on the 1830 US Federal Census, located in Harrison, Virginia in the Western District but it's been transcribed as Samuel Beverlen. It makes some amount of sense because Mary Mann was born in Virginia and both her parents were from Virginia. He's listed as between 20 and 30 in this record but there is no date recorded on the page. It's within the realm of tolerance. This record lists 1 free white male between 20 and 30, 1 free white female between 30 and 39 and 1 free white person under 20 (I'd assume their first child).
How I would proceed:
I would actually start searching the census records with all the names of the children. For example, the 1870 US Federal Census made it easy to find the family listing in Illinois by searching for Georgiana (spelled Georgeana on the census by the way) because it's relatively uncommon.
Then I start to make searches or refine them based on what I find along the way.
Georgianna is listed as 14 in that record so I know her approximate age and can use that information to know when to search for records containing her.
In the 1870 record, there's only Samuel, his 21 year old son Thomas, his 18 year old daughter Sarah and his youngest daughter, Georgianna at 14. I expect to see this since Mary died prior to this census and he'd not yet remarried.
He's listed as a farmer and has a real estate value listed so I know he's owned his own land. I can look for land deeds.
On this census, he's not listed either of his parents as of foreign birth but there's always a chance that's an oversight, but it's worth noting.
All three children are listed as born in Illinois, so I can hunt there for more information.
I use any alternate spellings of any names I find to search as well.
A bit of background for future use:
Wales used a patronymic naming system up until the 16th or early 17th century. Instead of sharing a family surname, children would be given the first name of their father as a last name. If John Jones had a son named Morgan, he would be Morgan Johns. You may also see "ab" or "ap" (son of) inserted - so Morgan ap John. This often became "Upjohn" later on.
The patronymic system did continue, in more rural areas, into the 2nd half of the 19th century, though.
There was also a tradition to add a sort of self identifier like a location or the profession of the person to the end of the name to help differentiate them but this wasn't usually found in formal documents. You do see it in some letters or such, though.
Wales, after the protestant reformation, was reduced to a small number of baptismal or first names and then, through use of the patronymic system, it has resulted in a surprisingly few Welsh surnames but it can cause complete havoc in research because none of the people in a single village with the same last name may actually be related!
www.uk.genealogy.org.uk has a lot of genealogy information on Wales. (http://www.uk-genealogy.org.uk/wales/index.html)
We do know Samuel's parents must have arrived before 1801 or he wouldn't have been born in the US, so I'd search probably 1780-1801, as sparse as those records are, for immigration or naturalization records for them. If there's a historical society in PA, somewhere near any listed location, I'd check there. It also pays to research general immigration waves to the US from foreign countries and what was happening in the world at the time. Most Welsh immigrating to the US were farmers or miners and a huge center of Welsh immigration was Pittsburgh, PA. So I'd probably focus searches in the Pittsburgh PA area to start with for Samuel's parents. I'd also use that as a place for immigration searches.
There's a whole lot of gut instinct and poking around involved in genealogical research and a lot of asking yourself if something you found makes sense. I always caution people to rely on REAL records for proof (not family lore or other people's family trees) but to be open to the fact that records are not perfect and there will be errors. The older the records are, the harder to find, the harder to read and the more errors or "liberties" you will find.
Also, keep searching. New records come online all the time and new people show up with their own searches that can intersect yours. It pays to keep hunting.