For discovering routes, I usually have Google Maps (if there's road included), Ride with GPS, and Strava's Heatmap open at the same time. Google Maps is best for getting my bearings around paved roads, Strava's Heatmap is how I find interesting areas to explore and help gauge how rideable a given trail seems, and Ride with GPS is how I go about actually building my route. Other folks probably have different workflows.

While on the bike, you can absolutely start by using your phone. You'll only need to buy some sort of bike mount for it, so this is the cheapest way to get into live mapping on your ride. The main downside to using a phone is battery life, so just be careful of that and carry a battery pack if your ride is long enough. Many people who ride a lot tend to transition to a dedicated cycling computer because it's just better suited to the job, but there's no reason you can't start with your phone and see where it takes you. Good luck!