The titles of Medieval British nobles varied depending on what part of the Middle Ages you are looking at.

Before the Norman conquest there were Earls in England and Thanes in Scotland and these were the only titles of nobility other than Royalty.

William the Conqueror introduced the title of Baron to England, and he kept the title of Earl. For quite a long time, these were the only two titles held by English nobility (other than the title of Duke of Normandy, claimed by the English Kings).

There were generally less than 200 Barons in England in the period between 1066 and 1300.

In 1307, at the end of the reign of Edward I, there were eleven Earls in England and Ireland.

The title of Duke was first created in England by Edward III in 1337 when he named his eldest son, Edward, the Black Prince, Duke of Cornwall. By 1483, there were 16 Ducal titles in England and Ireland.

The title of Duke outranked all other titles except King and Queen in England.

The first Marquess in England (above an Earl but below a Duke) was Richard de Vere, 9th Earl of Oxford, who was appointed Marquess of Dublin by King Richard II in 1385. He was later created Duke of Ireland, and the title of Marquess was eliminated. In 1397, John Beaufort, 1st Earl of Somerset was appointed Marquess of Dorset, but he fell out with the King, and the title was revoked in 1399. There were no other Marquesses created until 1442.

The title of Viscount (below an Earl but above a Baron) was created in 1440 when John Beaumont was created Viscount Beaumont by King Henry VI. This remained an uncommon title.

For most of the Medieval period, the only titles of English nobles were Earl and Baron. Between the conquest and about 1300, these titles usually implied rights over lands and a feudal duty to provide military support to the King.

In the later Middle Ages, the new titles of Duke, Marquess and Viscount first appeared. These titles appeared as the relationship between titles and land was diminishing and the titles were more of a recognition or an honor than part of civil or military administration. (Though, of course, title holders were generally rich and powerful men, and had a role through Parliament (if one was called) in civil administration, just not a role in administering civil judicial or governmental duties in regions of the Kingdom.)

The title of Duke became fairly common, particularly to bestow upon the sons of the Monarch. The titles of Marquess and Viscount remained fairly sparsely used in England, certainly in Medieval times.

I'll give the basics, since the better credentialed might regard the question as rudimentary.

The most straightforward answer regards the hierarchy. In ascending order: Baron (Viscount) Earl (Marquess) Duke. Those not in parens, the main categories. The parenthesized titles are rarer, and only introduced at the end of the period--in the 15th century.

The "job" for all these people is making money from their estates. From the production of serfs on their land. Though increasingly during the period, from agricultural rents. Their duties to the sovereign are mustering a body of troops for war. Otherwise maintaining a degree of peace and security on their lands.

In keeping with that, the nobility are not courtiers (though courtiers would be of noble blood--younger siblings, grandkids, cousins, and maybe the odd acknowledged bastard).

The titled nobility mostly stay on their estates, and could spend decades w/o appearing at court. You seem to be equating the hereditary peerage with some form of government officeholding. But this was rarely the case in the middle ages. And has never been a prerequisite for having an executive government job.

Wiki "great officers of state" for some of the oldest, senior government jobs. Among these, only jobs with a military role were commonly held by nobles. Because they are a land holding warrior caste.

Chief Justiciar sometimes noble. But the rest of the top administrative jobs (that we'd consider cabinet/ministerial) are usually held by church officials, or by commoners who have been successful merchants. Often bishops. Or a good way to become one--since there's no cause to object to religious promotions for office work. Our dual understanding of "clerical" as both priest and paper-shuffler attests to this.

In the later part of the period a commoner who did a good job might get a knighthood out of it. But extremely rare for anyone to get a peerage for clerical work (I expect there are cases, but IDK one pre-Tudor). This would offend noble warriors. Likewise the clerical work would be beneath them. Further, many would be unqualified. In the middle ages, being rich and titled is no guarantee of being literate or numerate.

Perhaps worth noting that desirable literacy for an administrator would be Latin throughout the period and French for most of it. English only became a language of governance later in the 14th cent.

In short, the importance of central government as a magnate magnet is post-medieval. At a later date more nobles became regular courtiers. But most have always retained greater connection to their lands than to Westminster/London.

At a later date high administrative responsibility became associated with the hereditary peerage. But even once the two became equatable, its been more often the case that the job got you the title, than the the title got you the job.