Craft stores are indeed a great first stop! The downside to this is that you’re going to need to be very specific in what you want and how you want it to be preserved. In the retail side of crafting, there are different levels of experience working there and some don’t care enough to learn more about what they’re doing to do a good job.
I’ve seen some handle every project like it was a relic. I’ve also seen some slap masking tape to the corners of a mat, press it into a frame, and call it a day. For something that’s autographed and meant to last forever, you really, really…really don’t want the latter, lol! Just be observant and do not be afraid to ask as many questions as you need to to ensure that your poster will be handled properly.
If you’re not near any craft stores there are also framing shops. I was actually surprised by how many there nearby! Most employees are artists themselves or have had enough experience on good framing standards to know how different materials need to be handled and secured.
Let’s say your poster was signed with a Sharpie (or some equivalent). Sharpies are solvent based, if they are used on archival paper, it will damage the paper, but there are options that can really slow the deterioration process.
You mentioned that your paper is glossy? If that’s the case I don’t think the ink will bind enough to the fibers to bleed out, (although there may be some) and they fade hella fast. But there are types of glazings that a framer can use to block harmful rays.
Of course, wherever you’re going to put your poster, keep it away from any direct sunlight (not directly across a window or someplace like that) where it will be exposed to heat and natural sunlight for long periods of time for risk of fading.
Whichever option you choose, you’re making an investment into something important to you, so don’t be afraid to ask questions until you’re satisfied with what you’re going to get.