What primer should I use to paint over nicotine stained walls

First you need to clean the wall thoroughly. It's always a good idea to clean your walls prior to painting because they pick up grime over time which will prevent the new coat of paint from adhering properly. In a kitchen, stains are more likely to be caused by splashes from food, so they could be greasy so it's even more important to clean first. Use TSP (tri-sodium phosphate) soap if you can find it; if not, there are enzyme-based substitutes that you can use which are OK.

You should sand the old primer, but not enough to remove it from the wall. You only want to roughen the surface so that the new primer has a better surface to hold onto. Make sure to wear a dust mask while you're sanding. Rub the wall lightly all over with sandpaper or a sanding sponge (which I use because they're washable and re-usable). You should see light scratches on the paint.

After you sand, be sure to wipe down the walls with a damp cloth to remove any dust from the sanding.

Finally, look for "stain-blocking primer". Make sure that the primer you choose will work with the type of paint -- oil-based or water-based (aka latex paint) -- that you're going to put over it. I've used Kilz to good effect; other people on this site recommend Zinnser Bullseye 1-2-3

The paint/primer should be fine, especially with two coats, but I typically begin with primer, as it seems (in my experience) that primer holds paint better and lasts a bit longer before requiring touch ups or repainting, and it's often cheaper to do a coat of good primer (match latex to latex, or make sure you follow the label if you use a different combo), then two or three even coats of less-expensive paint (paint+primer is almost always 2-3x more expensive than paint alone.

I wouldn't sand and re-paint, of course. You should be fine with what you have so far.

[Edit: one other note on paint+primer paints; make sure you read reviews or ask others about their experiences with the particular brand you're buying. A friend ended up with a patchy-looking paint job when he used one of the cheaper brands. I don't know if it was an isolated incident or if the brand is normally bad (or if he didn't mix the paint well!), but research before you buy.]