You do not need to prime the walls unless you are going from a flat finish to one with a sheen (such as eggshel/satin) as the color of your walls now most likely is darker than the primer would be. These dark red colors do not cover all that well as alot of paint companies make these colors in a tint base that is pretty much clear and they take multiple coats to get an even finish. You should cut in and roll one wall at a time and I think that a 1/4" nap will give you a better job, the only down side is you ahve to dip the roller more often.
Also check and see if the paint company makes the color you want in red base which will make a world of difference in the coverage.
Happy Painting.

Ah.....NO! Lets see - a 3/8" knap first of all - 1/4" doesn't hold enough paint.

Second of all - if it is a Ralph Lauren Paint color you have - make sure you get the RL Deeptone Primer to go with it.

It tints to a colour that is very close to the top coats.

With this primer you should be able to cover in three coats of finish - so that would be four all together......

Without a primer very close in colour (pink - or white) you could see 5-7 coats and still not get the correct colour or coverage.

Mr. Paint

I have found that with dark colors a 1/4 nap really give better coverage because it has fewer peaks and valleys, it is almost like spraying the paint on.

What exactly does the primer do? Also, what is this 1/4 nap stuff? If you can, please explain a little better, i am a rookie. Thank you so much

There is no reason to use a primer as long as you are using latex over latex or oil over oil paint.

Tinting primer is a waste of time and money.

Primer is not needed when changing 'sheen'.

The primer will seal up a pourus surface and you need that if you are going from a flat to eggshell/satin as the primer will seal the surface better than finish paint but if you go this route be sure to get a deep base primer because if you get a white primer all you will end up with is pink and not red. If you are staying with the same sheen (flat over flat or eggshell over eggshell) just apply the finish paint in the new color over what is there now. When you go to the PAINT STORE just ask for 1/4" nap roller ( they go from 1/4" to 1 1/4" ) and they will know what you are talking about.
Hope this helps out.