One has to assume the wizarding population of Great Britain to be fairly small. JK Rowling only mentions 7 male wizards in Harry's class. Assuming equal proportions of males and females as well as equal proportions between houses, there should be approximately 14 wizards and witches in each house, so 56 total per year. With seven years at Hogwarts, there should be 392 students total at Hogwarts. Let's give JK Rowling the benefit of the doubt and, assuming Harry's class to be abnormally small, let's say there are 500 students total.
This poses an interesting question. What fraction of the general population is wizards? Using the UK life expectancy of about 77 years in 1997, the total number of wizards would be about 4,300. Using the 1997 population estimate for the UK as fifty million, less than a hundredth of a percent of the population are wizards. This would explain the relative ease of keeping their existence secret and would perhaps suggest that some of the many Ministry of Magic departments devoted to protecting secrecy are redundant.
So if the retirement age is around 65 and 17 is the age of entry into the workplace, the workforce contains about 2,700 workers, ignoring stay at home parents and Muggle born wizards' parents.
According to Quidditch Through the Ages, there are 12 professional Quidditch teams in the UK. Oliver Wood tells Harry in book four that he has been signed to Puddlemere United's reserve team. Puddlemere United is described as a second-tier team in Quidditch Through the Ages, so each team must surely have a reserve team. Each team must then have 14 players, so 168 of the wizards in the UK are playing Quidditch. If each team has only one manager, then 180 wizards are involved in professional Quidditch. This reduces the remaining size of the workforce to 2,520.
Subtracting the number of teachers at Hogwarts, (28 named, minus Dumbledore who is well over retirement age), we hit 2,492. There are 26 shops in Diagon Alley, and we low-ball our estimate of employees per shop at six. While some shops are mentioned as only having one employee, for example, Ollivander's, the Alley is also home to establishments like the Daily Prophet, which has many more. Only one shop from Knockturn Alley is included in this calculation (Borgin & Burkes) and no street peddlers are assumed, so an average of 6 employees is reasonable and likely low. This results in 156 people working at Diagon Alley, bringing the total number of wizards in the workforce down to 2,336. There are 20 shops mentioned in Hogsmeade as well. If we again assume 6 employees per shop, which again is likely low since many are service-intensive, then 120 wizards work in Hogsmeade, bringing the remaining total down to 2,216.
Now we get to the big guns: the Ministry of Magic. Mr. Weasley mentions a task force of five hundred who worked on casting protective spells for the Quidditch World Cup, so there must be at least five hundred workers. The office of the Minister for Magic and Support Staff contains about twenty-five employees (including the minister himself and undersecretaries), which sounds reasonable. The Department of Magical Law Enforcement has the Auror office (which contains eleven named members and probably consists of sixty total), and many more minor departments, one of which, the Misuse of Muggle Artifacts Office, is specifically mentioned to contain only two workers. The Department of Intoxicating Substances probably has five (there's not a lot of drinking mentioned in the books) and the Improper Use of Magic Office probably has ten to fifteen. All in all, I estimate the whole department contains about two hundred employees, bringing us down to 1,975.
So since there's seven departments total, I subtract an additional 1,200, bringing the total down to 775. Factoring in the unemployment rate of 7 percent in the UK in 1997, that brings the total down to 585. Five musical bands are mentioned. The Weird Sisters consists of eight members, and we can assume the remaining bands contain at least four members. If each band has one manager, then 29 wizards are involved in music, bringing the remaining total to 556. At least one wizard-run radio station exists (the Wizarding Wireless Network), which must be run by a minimum of four people, reducing the remaining total to 552.
Healers who work for St. Mungo's must also be accounted for. Five floors are used for treatment, plus an upper floor with a tea room and gift shop. If five healers work on each floor plus two trainees, then 35 wizards are involved in treatment. At least four people must work in the tea room and gift shop as servers and cashiers (one for each job for the day shift and night shift), and at least two wizards must work as receptionists (again, one for each shift), then 41 people total must work at St. Mungo's at a minimum. This brings the remaining number of wizards down to 511.
So while we used minimum numbers in this estimate, we feel those numbers are justified because magic use cuts out a lot of menial tasks and reduces the need for employees. Therefore, we feel that the remaining five hundred cannot simply be unemployed. Instead, they must work in the surrounding Muggle communities. Because Hogwarts does not teach math, science, or any useful twenty-first century skill, and they cannot produce a reliable high school transcript, they probably work as unskilled labor. They are probably all Hufflepuffs. (We should note, however, that they can use magic to perform such unskilled labor, making their lives cushier than those of Muggles doing the same jobs.)
We have discovered dark secret of the Harry Potter wizarding world. Hogwarts does not prepare graduates for the real world, and instead teaches them the easy way out. But, really, wouldn't you be OK working in construction if you could also apparate?