In the UK, standard practice is to coat walls in your situation with a mixture of UniBond PVA Adhesive & Sealer and water (instructions on the tin will give recommended mixing percentages).
Then paint over everything with either:
- A watered down white wall emulsion mixture (again recommended mixing percentages will be found on the tin).
- A white "block out" wall emulsion.
Then paint your walls with your chosen wall emulsion colour. In your case, as it looks like it's a bathroom of some sort, I would go with a emulsion paint specifically for high moisture areas (such as bathrooms & kitchens). Doing so will have the benefit of lasting longer in those kind of conditions, also those specific type paints offer a lot better protection from mold forming on walls in high moisture areas.
Just throwing out a (crazy) idea you might also be interested in, seeing as you are leaving areas of exposed brickwork (not plastered over).
- Clean the exposed brickwork thoroughly, then seal that brickwork with an appropriate clear (waterproof) sealer.
- Then paint the plastered areas with your chosen colour (as per above recommendations).
The contrast between the exposed (sealed) brickwork and painted plastered walls can make for a great effect (if you like that kind of thing).