You should be able to use all that you have to get a decent setup with calculated power. Your speed and cadence sensors are good, you have a name brand trainer which should allow for virtual power without a power meter, but you have to check whether your app can support that.

I think if you start your app and have all of your devices up and running the app should find them.

As for phone vs. computer, it's the sensors that'll make or break the setup. Where computers work better is in battery consumption. Phone batteries don't last as long because, well, they're phones, gps, wifi, cellular, etc... A computer just has to worry about reading the sensors and the GPS if so enabled. For indoor training, where boredom will overcome you long before the battery runs out, you probably don't need a computer. For outdoors, on that all day ride, maybe you do. My wife tried using her phone to track running training and she would run out of power. She is very happy with her Garmin watch as she could run the entire marathon without worrying about it. She also has it interfaced to Strava, but she doesn't remember doing anything to make it happen. It just worked.