what is the best router to use with apple devices

Probably the router that your Internet Service Provider (ISP) offers, since there will be zero in the way of setup that you need to perform, and the ISP will fully support the product if there are any issues.

If you want to purchase a router on your own, then you will have to deal with the setup of the device. If there are any issues or problems, your ISP will blame the router. The router support folks will blame the ISP.

If you decide to purchase a router on your own, we need more information from you about what you might mean by "best".

Best performance?

Best price?

Best value?

Best ease of setup?

Best security?

Best warranty?

Best styling?

Best something else?

FWIW, I would suggest routers from either Asus or Synology if you are looking for a simple one-for-one wireless router swap-out with your current router ... which I am assuming is an Apple AirPort base station.

What would be "best" should be based on your overall networking requirements ... which you haven't provided. Without them, I can only assume what they could be and would suggest that you check out SmallNetBuilder's Router Ranker to get started.