Very important! For many reasons, not least of which is the large area of ceiling and walls that will be painted. You will want colors that coordinate well with furnishings and with each other if you choose more than one color for a room.
Additional issues with paint may involve whether you prefer non-VOC (Volatile Organic Compounds) paint, as many people have health issues from the off-gassing of traditional paints.
In areas subject to dampness such as bathrooms, a paint rated specially for kitchens and bathrooms would be best, in an easy to clean satin or semi-gloss finish.
Selecting the colors:
Sherwin-Williams has a neat site where you can upload a photo of a room you will be remodeling and painting and it will automatically color the walls (even half-walls) with colors you select, so you can see what it will look like before purchasing any paint!
Behr has an equivalent on-line program where you can upload your photo and try out different colors effortlessly!
It is great to be able to hire someone to actually do the work. Taping around the trim, covering the flooring and furniture can be more than we want to do.
The photos are from Room Color Idea. I find that just looking at paint swatches, no matter how well presented, are hard to visualize on an entire room. In addition, seeing what others have done give me ideas that I might not have come up with on my own.
So check out the room colors that others have used and try them online on a photo of your room, then get going and select some paints to liven up (or maybe tone down) that room.