So we get Misters Baggins, Took, Brandybuck and Bolger - all Gentry; and commoners such as Master Sam Gamgee, and the Farmers Maggot and Cotton.
What is interesting is that the Hobbit Family Trees in the Appendices, show that the Shire Gentry intermarry pretty exclusively - so that the Frodo, Merry, Pippin and Fatty Bolger are all inter-related (and with the Boffin family, such as the 'extra' Folco); but not related to Sam. And Merry marries Fatty Bolger's sister; Pippin marries Diamond 'of Long Cleeve' - thus, presumably another of the landed Gentry.
But Sam (regardless of his achieved heroic status, fame and wealth) marries a commoner (Rose Cotton). And Sam stays Master Gamgee, despite becoming the Mayor; which suggests a distinction between the elected positions such as Mayor, and the hereditary positions such as Thain (held by the Tooks at the time of LotR) and Master of Buckland.
Indeed the Thain and Master are essentially titled aristocracy. Pippin and Merry are heirs to these premier lordships, and therefore perhaps the two highest status young Hobbits in the Shire.
However, while Sam remains Master Gamgee apparently up to his death; we can see that at least two of his children become Gentry - Elanor marrying Fastred 'of Greenholm' and the first Warden of Westmarch - a western extension of The Shire equivalent to Buckland in the east. Goldilocks marries Faramir, Pippin's son, and therefore becomes wife of the Thain - the Shire's premier aristocrat.
The upwardly-mobile Gamgees illustrate that The Shire is a class society, but does not have a caste system.
There was a splendid supper for everyone; for everyone, that is, except those invited to the special family dinner-party. This was held in the great pavilion with the tree. The invitations were limited to twelve dozen (a number also called by the hobbits one Gross, though the word was not considered proper to use of people); and the guests were selected from all the families to which Bilbo and Frodo were related, with the addition of a few special unrelated friends (such as Gandalf). Many young hobbits were included, and present by parental permission; for hobbits were easy-going with their children in the matter of sitting up late, especially when there was a chance of getting them a free meal. Bringing up young hobbits took a lot of provender. There were many Bagginses and Boffins, and also many Tooks and Brandybucks; there were various Grubbs (relations of Bilbo Baggins’ grandmother), and various Chubbs (connexions of his Took grandfather); and a selection of Burrowses, Bolgers, Bracegirdles, Brockhouses, Goodbodies, Hornblowers and Proudfoots. Some of these were only very distantly connected with Bilbo, and some of them had hardly ever been in Hobbiton before, as they lived in remote corners of the Shire. The Sackville-Bagginses were not forgotten.