Is it a good idea to dedicate a page to thank people on a personal website?
That seems like a strange idea. People will wonder why you have made a page like this when nobody else does. And they might think you are just trying to show what a wonderful and grateful person you are. 

If I was you, I would just thank people privately or in the acknowledgements sections of publications. Journal articles can have acknowledgements sections as well.

If you really want to express these thanks in a public and long-lasting way, just write one sentence, or a short paragraph, and put that at the bottom of a page on your website that has your academic biography or some paragraphs about your research interests. Then it won't be in the way, and people will easily be able to ignore it. Make it as short as possible, and write it so that it is interesting (or as interesting as possible) even to people who don't know you or the people you are thanking.