What is the difference between Regular edition, Artist proof, Collectors Giclee and Museum Edition Giclee. I know the retail cost escalates from the artist proof to the Museum Edition, but other than price, which one will become more valuable through time? Are BOTH the Collectors and Museum Edition Giclee's signed and numbered?

Giclee are only second rate reproductions, so no value at all. These are not signed and numbered. Artist proof, signed and numbered is valuable (depending on the artist of course) but Museum edition signed and number is worth more.