The suggested Kodak chemicals are perfectly fine.
Just in case someone is not able to obtain these specific chemicals, some general suggestions:
*) Avoid all-in-one-kits; for a home user it can be reasonable to single-use the developer, but single-use of bleach and fix would be plain stupid (both un-economical and un-ecological). So you either waste stuff or you end up with unused components.
*) Avoid Bleach-Fixes for C41. They are unreliable, overly expensive, and also un-ecological.
*) The only thing you REALLY need is a usable C41 developer. Unmixed and protected from air (and light) it is quite stable (in fact, only the developing agent itself is prone to degradation), so there is no problem buying larger quantities. Exen mixed developer (stored properly) is quite stable; one could try to mix it as 2x concentrate for improved keeping.
*) Other components can come from alternative sources: Ferricyanide bleach can be made up at home following simple protocols from the internet. And any near-neutral pH BW fixer (not too acidic) can be used for fixing.

And, BTW: There are many variables in home C41 processing; you will have to optimize the process for your own needs (add or cut a few seconds), and it is a good idea to have a film developed by a good lab as a reference.