If you already have a frame you like, as long as it's larger than the print, it's easy to get a custom cut mat and it should only run you about $20.
Simply bring the print & the frame to a local art & frame shop like Michaels or AC Moore and have them cut a mat to fit. They will also be able to assemble it for you with archival materials.
A general guideline in choosing a frame is to make sure there's at least a 2" mat around the edge on all sides, so a frame for an 8x8" print would be a minimum of 12x12". Square prints can look good in either a square frame or a rectangular frame, it's up to you. Just remember to keep at least 2" on either side, in general a very thin mat does not look very good. You can always go wider than 2" depending on your taste.
I recommend using an archival cotton rag mat that's at least 4-ply. This will keep your artwork looking good for years to come and will not damage or discolor the print over time. My prints are all acid-free and archival, and if kept in archival mats will easily last a lifetime.
Here is a nice video from the website 20x200 which lays out how easy it is: