Warranty card dated mid-1990, and the watch looks like a 3590.50 from that era, but the warranty card also has a strange number written in the "ref" portion - looks more like a serial number than a reference number, and the serial would be from a much earlier watch. (maybe somebody smarter than me can explain that). I assumed the blue areas on the caseback are old plastic easily removed, or just camera artifacts.
Melanie, the good news is that the watch is all original, very good condition, with box and papers. That's what buyers are looking for! Also good is that the dial/lume is nicely aged and the caseback is very clean. By any chance is there engraving on the side of the watch case? If so, that would indicate its a 20th anniversary Apollo XI limited edition. I'm assuming not since you did not show any pictures of the left side watch case, and thus it probably is not engraved. So, on the downside, this is not a particularly interesting Speedmaster in terms of date or reference number, its not a limited edition, its your standard Moonwatch (but still very nice and valuable), and it will need a service before someone starts wearing it everyday. I see this selling in the $2500 - $2900 range, can't really see this going over $3000, but you never know. If you had a value in mind, I'd say list it in the for sale section of this forum (with moderator approval since you are new here). Otherwise, I agree with others, Ebay with $1 starting price and no reserve.... have no doubt, this baby will sell at a very fair market value, if not a premium if two or more really want it. My guess would be around $2900 USD. you may even get a few offers in your inbox here on the forum, I would be interested, but I am already broke from buying too many watches
馃榿 Best of luck.