I have several questions.

First, are the nails galvanized or stainless steel?
If they are galvanized, I would prime them first with Ospho before caulking and then prime with a regular primer. Ospho is a green liquid that will turn rust black and prevent bleed through on your paint. Galvanized nails rust fairly quickly and this will head off a problem in a year or so down the road. You can also use Hammerite Rust Cap Primer for the nails. (Many painters tell me that QTips work great for applying Ospho). If they are stainless, I would caulk first and then prime the surface. This will prevent any flashing effect from the Ospho on the finish coat. I would actually prefer to use a spackling compound that will stay somewhat flexible, but you can use caulk also.

Is the siding a hardi-panel or hardi-plank? I have not seen any real wood siding pre-primed in my market. If it is hardi-plank, I would prime the siding with a good latex 100% acrylic primer. You could use 123 by Zinsser, Suprime by Pratt and Lambert, or FreshStart by Ben Moore and then topcoat with your choice of paint. Every paint company will manufacture a 100% acrylic primer to use with their topcoat. The primer used on siding as well as steel doors is to protect the product in shipment. It is still intended to be primed before painting. I would highly recommend that your primer be manufactured by the same company as the paint for warranty reasons.

Make sure you use a really high quality caulk. I have found that Big Stretch Caulk by Sashco is the easiest to work with of all the caulks on the market. It is paintable. It is a little expensive, but is very flexible and smooths out great.

Consider having your primer tinted 1/4 to 1/2 formula of your topcoat color. It makes the paint cover better. The primer will still be a little light to the finish coat so you can see any areas you have missed when applying your topcoat. I do recommend two coats of finish paint.

Most painters prime than caulk, but I don't like the texture of the primer when I'm smoothing caulk over it, so I caulk first. Personal preference, really.

The general rule is to prime first and then caulk because caulk will stick better to the primer than to any other surface. Also, I think there is too much advice on the internet and other places by the 'pros' recommending that nail holes be filled with caulk. That is just not what caulk is for. If your goal is to get the nail holes to disappear, then caulk is the wrong thing to use. Because caulk shrinks so much, it is virtually impossible to fill a nail hole of any size flush with the surface, so it will never disappear...you will always see the holes as pits. You can use an exterior spackle or putty and there is also shrink free exterior spackling that you can buy that is sandable. It's not really shrink free, but you can overfill the holes and then sand flush when dry.

as a professional, I always fill the nail/screw holes with caulk, immediately using a flat edge anything to flush it up, then move to the next one. Looks flawless when dry. Never have to put more in, the flat edge squishes the caulk into the hole.

so with two quick movements after applying caulk to a few holes, use the flat edge to squish/press in, then the actual edge to flush it to the outside edge of what you're caulking. Wipe the excess off the flat edged item you're using and move on.

Have used flat edge of
flat Simpson tie, thick flashing, etc. - metal works best.