After you get a good idea of what you think the fair value for your watch is, you will need to decide where and how to sell it. I think you have a couple of good options, depending on your level of comfort, and prior experience doing these types of transactions. No one way is better or worse than the other, each has its pros and cons. My one caution to you is this: be on the lookout for scammers, now that people are aware you have a nice vintage Speedmaster you will start to receive private messages, some legit, some not, from potential buyers. Be skeptical, and take no chances in the sale of your watch. With that my thoughts are:
First we have a marketplace here on omegaforums.net (there are also other watch forums that provide online marketplaces to sell/buy watches, all work similarly). As a rule, on omegaforums, you need to have a minimum post count, which you do not have; exceptions can be made in rare circumstances, you would need to discuss that with any of the moderators here. To sell online requires some level of expertise, posting pictures, answering questions, taking payment online (unless you find a local buyer and can arrange a face to face), and also shipping. Shipping a high priced item can be complicated if you haven't done it before, especially if you are doing so internationally.
Another way is to consign your watch to an auction house, such as Christies, Antiquorum, Sotheby's, etc. Each of them describe in detail how it works on their respective websites; but typically they will appraise your watch and you mutually agree on the terms of sale such as the minimum you will sell for (aka reserve). The auction house will take a percentage of the sale, this can be negotiable if your watch is particularly nice and will enhance the overall auction. The benefit here is that they do pretty much all the work, and there is potentially a bigger price upside (although their take is usually around 15%; the downside is that you typically have to wait several months, for the next auction and there is no guarantee it will sell. Many people sell watches on Ebay, I do not, and would not recommend doing so for various reasons.
You can probably sell it locally as well, through a local reputable watchmaker or on local marketplace sales listings; this is really hit or miss, local watchmakers are unlikely to give you anything close to fair market value as they will be looking to buy wholesale and re-sell the piece. Local collectors would be very interested, would pay more, but are sharp buyers and know how to negotiate, so you need to know your stuff and know the value of your watch.
We all look forward to pictures of your watch, and will virtually drool all over it if its as good as you suggest it is ;-) Welcome to the forum.
