well i did a horizon spidey some years back. this should be the same.
prep and primer as usual. on my spiderman, i decided to go with a very dark, almost black blue. so i basecoated the entire model with flat black, and airbrushed highlights on all the muscles with a flat navy blue. (if you are going for a more of a modern comics appearance, simply substitute the balck with navy, and highlight with a bright blue.) once dry, it was sealed with dullcoat. allow to dry 24 hours.
the blue sections were then covered with latex, masking them off. the red areas were basecoated with burgundy, and then highlighted with insignia red (both colors flat). once dry, the latex was peeled away, and the entire figure was again sprayed with dullcoat.
the inside of the eyes were painted flat white. i then filled a 0.5mm technical pen with black acrylic ink, and traced the web pattern and the lines separating the red and blue areas, allowing the grooves to guide the pen tip. the outside of the eyes were painted with flat black. once again the entire model was given a coat of dullcoat.
finally pearl white was painted over the white part of the eyes.
thats it. on the new spiderman, i might try wrapping the model in some sort of fine mesh screen before applying the highlights to recreate the tiny fishnet pattern on his movie costume.
I built the arms and legs and then cleaned up the seams on all the parts. Then I sprayed the red and clear coated with semi-gloss to give a smoother surface for the drawing of the web pattern. I used a Rapidograph Technical pen #00 to Draw the web details and when dry sprayed another coat if clear. Then I masked off the red and sprayed the blue. Once dry, I glued the arms first and then the legs to the body front. Tape or rubberband the back half to the front to be certain the placement is correct while it dries. Once that is completely set, I glued the back to the front assembly and use blue masking tape to get all the seams to fit. Once that is completely set I sanded the seams lightly and filled any voids, sanded again and then air-brushed the blue and red to clean up the seams. Last I glued on the head front and cleaned all the seams and then went back and re-drew the web pattern. Sounds like a lot of messing around but it pays off in the end. I'll post photos of my Spiderman as soon as I can get it photographed. Hope this is helpful.
I just use Gunze Panel Line pens for things like the web... Gunze makes very very fine tipped marking pens for outlinging panels on model kits. They come in black, brown and dark grey. I haven't bought them lately but they have several styles and formulas. Some are what they call "wipable" so you can run them down the panel and then wipe the outside of the model to clean off any excess. They use them a lot on Gundam kits....