If read that you can have that profesion, but I don't see it when I create my character.

There are relatively few starting professions. You only get to see the full possibilites once you start the game properly.
In the character actions menu (click on name) there is an item for 'occupations'
When you have 8 action points saved you can use this to switch professions (and after a few generations keep a track on what professions you have trained too lol).
You need to start as one of the base professions and then switch to guardsman via this method whenever you have the resources to do so.

Oh, I see.
Which profession would be the most appropriate/ easy to get to guardsman?

The smith I found good to start with since the goods were cheap to make to build up some funds and tended to sell reasonably well....
At any rate it's a matter of saving funds to buy an appropriate property for the profession (build or buy an existing one) and saving action points to make the switch to any new profession.
Edit: Of course if you marry for wealth /cough it is easy and quick to get funds to buy/build appropriate property for the new business anyway so it's just a matter then of waiting a few turns or so for teh AP to build up.

You mention an appropriate property for the profession, which one is the one I want for a Guardsman?

"Appropriate property" means the building for a specific profession. For the Guardsman, it is the Guard House. Once you bring up the Build menu, you'll see different types of buildings, but you'll only see buildings which you can build with your current professions (this means that you'll only see the Guard House under "Defence Installments" (?) if you have at least first grade in the Guardsman profession).

This might be a stupid question, but, before changin jobs I need to win the election for Nightwachman, right?

Nope, that's the political career; your professions are a separate thing, even if they sound to interfere with each other.