There are still some iPhone 4s models floating around. That would be the oldest I would go since iPhone models prior to that don't support Bluetooth 4.0 (or BTLE as it's known by). You don't need the Bluetooth unless you decide to get sensors like a heart rate monitor and/or a speed-cadence senor. I'm not sure what Android phone would be the oldest model you can use for what you want, since I have only owned iPhones. As for cycling apps, there are a ton out there for both platforms. Almost all have a watered-down free version and a subscription version. The difference between apps is the features and functionality and whether or not it has a monthly or yearly subscription.

Since you don't already have a smartphone and might be considering sensors in the future, you may want to look into the Garmin line of GPS computers. They are certainly pricier but worth it if you don't already have a smartphone.