To start from the beginning: you purchase some combination of hunting/recreational license that includes a deer tag. You do not have to specify weapon choice at that time.
If you wish to apply for special permits in the spring (like second deer tags), then you must select a weapon type before applying: modern, muzzleloader, or archery. You may only apply for special permits that match the weapon type you selected.
If you do not apply for any special permits, and if you already selected a hunting method you can exchange it for a different hunting method before the applicable season starts.
If you apply for, draw, and purchase a multi-season permit you may apply for special permits in any hunting method category. You may hunt all the general seasons, but only with the hunting method applicable to that season. In other words, you can hunt the general archery seasons but only with archery equipment.
Hope that helps.