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.
good luck!