Am I correct when I say the walls have dull and not dull sections? It appears that way looking at photo #3 on the upper left wall.
If that is your concern (having the walls painted with a consistent sheen) than you will need to re-paint them.
I've found most paints can be judge for quality on how much they cost (most of the time). Choose a reputable brand of paint (there's alot) that's within your budget. $30-40 USD per gallon is common.
Choose the type of paint. You'll need an indoor latex ...eggshell, flat, semigloss?. Choose a paint that is a paint and primer in one can. I've found this type of paint to be much better at covering an old color in one coat. It contains more solids and binders so it will be thicker and cover much better than a paint with no primer. It's usually not much more than a regular gallon of paint.
Some suggestions for a quality paint job:
-If you will use more than one gallon of the same paint color mix them together so the color is uniform.
-wash/clean the surface to be painted. No rinse TSP is a good grime cleaner and should be used before paint is applied.
-use a 3/8-1/2 inch napped roller pad. Any brand will work. Load the roller fully and evenly with paint. Apply the paint with the roller in vertical lines that slightly overlap the wet edge. Re-fill often or if you find yourself applying force to extract paint from the roller.
You shouldn't need more than 2 coats of paint to cover the old color unless it's very dark. To cover the sheen problem in your photo's one good coat with a paint and primer should suffice.