Many of the jobs open to a 17th century Londoner would seem familiar to us today, albeit with slightly different titles. Taverns and public houses, for example, had barkeepers, barmaids and 'potmen' (the male version of a barmaid). There were lawyers, clergy, physicians, domestic servants (cooks, maids, housekeepers). You could drive people in a 'hackney carriage' - the 17th century version of a taxi driver. You might be a 'night soil man', emptying cesspits and privies - our modern sanitation worker. You might be a soldier or a sailor - or a thief or prostitute.
You could own a shop - although a key difference between the 17th century and today is that you would often make the goods you sold. You would also be likely to live in or above your shop, unless you were extremely successful. Before the mass industrialisation of northern and midland England in the later 18th century, London was a significant manufacturing centre. And so you might make and sell watches, furniture, hats, books, scientific instruments, jewellery, kitchen pots, saddles... anything you can think of, really. Some shopkeepers were wholesalers, particularly in textiles and fancy goods - i.e. they bought and sold cloth directly from weavers, also in London.
Entry to skilled jobs was tightly controlled by the livery companies of the City of London - effectively, trade guilds - who laid down rules regarding apprenticeships and quality control. Of course, the majority of jobs, skilled and professional, were only open to men at this time. Women could weave, sew, clean, cook, serve food, act on stage (after 1660), and teach children. There weren't many other independent options, although many wives and widows traded in their husband's name, often inheriting a business and carrying it on successfully.
Some jobs which existed in the 17th century have no real modern corollary. The barber-surgeon, for example, was someone who could cut your hair and shave your beard, but was also qualified to perform dentistry and minor operations. (Hopefully not at the same time). Patten-makers manufactured iron and metal overshoes, which were worn mainly by women to preserve their thin leather or silk shoes from mud and rain. Ballad singers would walk the streets, singing the latest political or humorous ballads, selling the printed lyrics to interested passers-by. Ostlers looked after horses in public coaching inns.
In terms of what jobs were most common - most men would have worked at a skilled trade, usually as an apprentice or a qualified 'journeyman' for a master craftsman or merchant. The very poorest would have been casual labourers at markets, building works and docks, sailors, and even beggars. The wealthiest (of those who actually worked rather than living off a landed income) were professionals such as lawyers, and substantial merchants. Women, as I've said, had fewer options, but were most commonly to be found working in private domestic service as cooks and maids.