Hiring a hero to be your mayor has an effect on your town. It can speed up the time it takes to build structures or train troops. The statistics of your mayor determine how much it speeds up:
Mayors with high Politics (POL) affect the building times of structures, the collecting of resources, and the building times of defenses on your walls.
Mayors with high Intelligence (INT) affect the speed of researching items in the academy.
Mayors with high Attack (ATT) affect the rate at which new troops are trained in the barracks. Strangely enough they don’t affect the speed of building defenses like archer towers.
You should only recruit heroes with at least one stat of 60 or higher.
The level of the hero is irrelevant. Only the statistics matter. A level 15 hero with a highest stat of 45 is worth less than a level 2 hero with a 62 in one stat. In fact you pay for heroes based on their level so a low level hero with high stats is preferred.
Politics helps with building your city and gathering resources.
Intelligence helps with spying and research in your academy.
Attack helps with fighting battles and defending your city.
Recruit only heroes who have a score of 60+ in at least one stat: Politics (POL), Intelligence (INT) , or Attack (ATT). Ideally in the beginning you want to find a hero with high POL to help you build structures faster and gather resources faster.
Theoretically you could recruit your first hero with less than 60 in a stat but you’ll want to “release” him as soon as you find a hero with a 60+ Politics.
You might for example find a hero with a 45-50 in Politics. It’d be better to have a hero with decent politics even if the score isn’t that high. At least you’ll receive a small benefit in building and gathering resources. After a little while you may find a hero with a 60+ in Politics. At that time you can release your hero with the lower politics score.