Buy the smallest cable possible, with twisted pairs for reduced attenuation. cat 5e / cat6 is a designation for RJ45 cables so they don't apply here
Good indication you have an issue with the outside connections I had a similar problem years ago whenever it rained my internet slowed to a crawl, They found the connections outside at the house leaked and corrosion got inside, when it got wet it caused problems
I would really appreciate someone with more know-how than myself taking a quick look at those links, as I can't always tell which is better value, very much appreciated.