I just set up Redis on a site that has been having some performance problems, and it seems to be running well so far. Does anybody know if it would be recommended to also run the Internal Page Cache and/or Internal Dynamic Page Cache module(s) in addition to Redis, or is this redundant? There isn't much documentation around yet regarding Redis and D8.
The Drupal modules decide what to cache (and for how long etc), Redis is just where the cached data is stored.
Having both/all enabled is not inherently redundant (though as 4k4 noted in the comments, there's a theoretical chance that one cache will improve speed so much that it renders the other redundant in terms of further speed improvements).
Enabling the lot will probably be common practice, and if not with Redis as the storage backend then Memcache, etc.
As said before Redis is just a "bin" where to store cache, it should be faster than the database bin (default Drupal cache bin).
These two modules are enable by default on Drupal 8, it is safe to let then enable.
For more details see the Berdir presentation : https://md-systems.github.io/drupal-8-caching/