Hello Kamil,
I’d like my opt-in box to be visible just above my blog roll and blow the header and the menu.
If you want to add opt-in box below the menu (site-wide), than loop-meta can be a good starting point. We have included loop-meta just below the menu which displays relevant sub-headings according to template like Blog, Category Archives etc.
So, you may place your opt-in box in that file or may include a new one if you have little bit idea of programming.
Also, do I need the raw HTML, or the short java script will do? Please, be very specific to what command to use if code change is necessary (CSS etc).
It all depends the interface of your opt-in box. It may very simple to complex including CSS, Javascripts etc.
Do you also have any recommendation for opt-in as Light box, pop up or exit pop-up?
Kamil, there are several free and premium opt-in Plugins. You may choose them depending on your need like,
http://wordpress.org/plugins/optin-revolution/
Thanks