In my homebrew, a wizard normally begins their studies at age 8, learning dance, reading, ancient languages, calligraphy, cooking, sleight of hand, to play musical instruments and various other preparations for the act of spell casting. Typically, the child will also do simple chores and menial labor for the wizard. Barring the rare prodigy, they will learn their first spell at between age 11 and 14, depending on the temperament of the master and how willing he is to put up with the hijinks and foolishness that comes with mastering one's first simple spells. Female students generally master their first spell about a year before male students, though by age 18 any gaps in ability have generally closed. Serious magic, of the sort more dangerous to the caster than a cantrip, is generally not attempted before age 16. By tradition, the apprentice stays with the master for 8 more years, leaving at age 24, however this long period of training has a prerequisite that the master and student get along - which is by no means assured. Some apprenticeships end as early as 18, with the apprentice left to fend for themselves with only the most meager possessions and skills. Others from more prestigious wizards who are perhaps have more opportunity to be selective about their apprentices go the full eight, at which time the master traditionally presents the student with a simple but useful magic ring as a token of his esteem and as a reward for their hard labor. These rings may be of new manufacture if the master knows the art but are quite often handed down from master to apprentice over generations if the apprentice is especially favored.
PC's are generally considered to be newly released apprentices, usually but not always ones that have not finished their full term of service for whatever reason - death of master, departed on bad terms, wanderlust, etc. As such it would be typical for a human PC wizard to be somewhere between 18 and 24. Note that this trope is partly to ensure the PC's don't have a patron and partly because a character that spent 8 years in study might well be 2nd level, but I wouldn't be hard and fast about it if the player wanted a particular backstory.
A typical master is 4th to 6th level, and in a human typically above age 65. Hedge Mages tend to be on the lower end of that scale, but they often take their own children as apprentices and so are typically not as elderly. Octogenarians of poor health and prestigious power (7th or 8th level!) are something of a trope, as it gives the ability to put a fairly high-level character into the setting without the expectation they'll be delving into a dungeon.
