Device compatibility + set-up?

Apple TV and Roku are just two separate devices connected to a TV.  They don’t need to know or care about each other.  Just like any other media devices attached to a TV (Blu-rays, DVDs, cable boxes, etc.) you just plug them into TV HDMI ports and switch the TV to the input you want to use at any given time.  I normally prefer to use the remote for each device but some people prefer various universal remotes.  As long as you avoid Roku “stick” models, then you can use universal (IR) remotes to control them. I don’t know whether Apple devices use IR remotes or something else.  (If “something else” then it will be harder to use universal/third-party remotes.)

There is no inherent monthly charge for using a Roku device.  However, out of the thousands of channel/apps available on Roku, some have fees and some want you to authenticate with a TV provider (such as cable) – however authentication only works for channels that they are already providing – not for adding channels.  Some of the channels you specified will want you to authenticate through your TV provider (which it sounds like you can’t) or set up some TV provider on your Roku.  For example, this site, suggests that “Sling Blue +PBS” would be a package that includes those three (plus 42 additional channels).  I’ll point out though that Sling is also available on your Apple TV device.