When I dusted off my old Bridgestone and decided to get serious again... I bought a Topeak Panobike cadence sensor and I installed the "Panobike+" app on my two iPhones (work and personal). That app has a nice "bike computer" dashboard. As I rode, I could easily see cadence, road speed, distance-traveled, average road speed, and average cadence. At the end of every ride, I could see a map of my ride and statistics for my ride. That might be all you need. But I downloaded every single ride to Strava anyway. The free version is great for reasons others have listed above.
I liked having the app on two phones because that gave me a back-up in case one had a weak battery or whatever... but I never found a way to sync the two. A ride's data was only on one or the other.
I upgraded to the paid version of Strava when I got a heart rate monitor... and I think the combination is brilliant and for me it's absolutely worth it. Now, I have a better appreciation of the line between under training and over training. Also, I'm motivated to compete, and I can define segments.
Topeak's cadence sensor is quite good, but their heart rate monitor disappointed me. (It would stop recording mid ride... and also it ate batteries.) I switched to a Wahoo heart rate monitor, and I believe it's categorically superior. One big advantage is that it has two LEDs on it: one tells me it's paired to my phone, and the other blinks with my pulse.
At the same time, I switched to using Wahoo's "Fitness" phone app. I think it's just marginally better than Panobike+. Like Panobike's, the Wahoo app has a good dashboard and it shows me my route and it logs my rides and statistics for each ride... and I still download every ride to Strava.