You don't need a dedicated cycling computer. If you have an Apple Watch and the Strava app on it, your rides flow into RideTool automatically.
That's it. No manual sync, no extra steps.
What you don't get without extra hardware: power (needs a power meter), cadence (needs a sensor).
The watch's optical sensor works well most of the time but can be jumpy on the bike. Road vibration, grip pressure, and cold all mess with it. If accurate HR matters to you, a chest strap (Wahoo TICKR, Garmin HRM-Pro) paired to the Strava app via Bluetooth is a big upgrade.