Custom framing doesn't have to be expensive. My favorite way to keep things affordable while still being able to completely customize everything is to use an online custom framing shop. You choose the frame, mat, and sizes and they custom make everything for you, and send you the joined frame plus everything else you need. You assemble it yourself, and save a ton of money doing so.
My prints are all archival, and I highly recommend making sure the mat you use is also archival and acid-free. When your purchasing your mat, it is best to avoid "paper mats" - this type will usually start to turn yellow after just a few years, and can cause your artwork to yellow as well. A cotton rag mat is always your best choice.
Maybe you already have a frame you like, or you've found an antique frame that you'd like to use. You can use any frame that's bigger than your print if you have a mat custom cut to fit.
Here are some instructions on how to get a mat custom cut to fit any frame.