Usage Recommendations

In the Types & Sourcingsection are breakdowns of many commonly used tapes paired with sourcing information, as well as some niche options that can be found if you know where to look that offer significantly better results. Rather than making you sift through all of that if you are just looking for quick recommendations, here is a table of each use case and the foams I would recommend, in order, with links to their respective breakdowns:

Adhesive/Method	Notes
Double-Sided Tape	Easy to apply. Great for repairs, stab tips, guards/crosspieces, getting other tape to stick better, and for securing handle wraps. You could build an entire weapon with this as the only 'adhesive'. Depending on the use, it is not as long lasting as actual adhesives. Should be used selectively.
Duct Tape	Easy to cut, tear, and apply. Can be very effective as a skin and is highly resistant to wear. Cheap versions are not worth it. Should never be present on striking or incidental surfaces. There are options that do all of the things that Duct Tape do well without being nearly as heavy (Strapping Tape with perpendicular Fibers, specifically). If better options are had, should generally be relegated to covering seams and skinning parts of shields.
Gorilla Tape	Better Duct Tape. While generally a straight upgrade to Duct Tape, sometimes you may find that it pulls away from surfaces where the tape was under tension or could buckle until you've pressed it back down a few times.
Packing Tape	Easy to apply. Only used as a skin for striking surfaces. Provides adequate protection from the surface of your striking foam tearing. Generally doesn't adhere extremely well, but is often good enough. Can make weapons "slappy".
Tyvec House Wrap Tape	Only used as a skin for striking surfaces. A thinner, elastic, upgrade from packing tape. The thinner material, plus its elasticity, make for a much more forgiving strking surface that has less slap to it.
Strapping Tape (Parallel Fibers)	Used to provide structure and stability to parts of weapons, primarily stab tips, guards, and axe/hammer heads. The fiberglass reinforcement makes the tape much more rigid and doesn't allow it to stretch, which can stiffen striking surfaces, so usage should mitigate how much coverage and how many layers are applied on striking surfaces. All of the fibers being oriented in a single direction means that it is only resisting stretch parallel to those fibers.
Strapping tape (Perpendicular Fibers)	Easy to apply. Used to provide structure and stability to parts of weapons, primarily stab tips, guards, and axe/hammer heads. While thicker and more rigid than packing tape, the perpendicular arrangement of the fibers in this tape makes for a thinner and more-flexible material than similar with parallel fibers, and it is more forgiving when applied on a striking surface. The fibers being oriented along two directions, and the tape generally being much wider than the kind with parallel fibers, allows for creating more stability with less built-up tape that you would see otherwise.
Cloth/Fabric Tape	Easy to cut, tear, and apply. Used primarily as a skin for incidental padding, courtesy padding, guards, and pommels. Also used to secure covers to weapons, to coat handles and exposed cores, and to cover seams/stiffer tape on striking surfaces (under the cover). A relatively strong tape, extremely durable in the face of constant abuse, moisture, dirt, etc. Not all fabric tapes are made equal.