I'm in no sense fit, and have weight to lose, but I manage a 7 mile ride (to work) in somewhere between 29 and 45 minutes wall-clock time.
For me, the best encouragement is to see what you can do now, and then see how it improves with time. We're all different shapes/sizes/ages/fitness levels, but if you find a circular route that takes you say an hour, do it regularly, see how long its taking t get to the various points round it, and start to chase those points, aim to beat your "average". Wind/traffic/tiredness will conspire to stop you, but it gives you something to aim for.
Commuting, I find having someone in front of me is a big encouragement. If they can cycle at that speed, then it means its worth me trying to. With some, I aim to keep them in sight until the roundabout. Others, I aim to overtake before the roundabout! I haven't found anythinglike another cyclist to encourage me to cycle consistently faster.
However, at 51, and 15 stone, I don't think I'm really cut out for the group cycle rides (and tbh have other things to do with my evenings and weekends).
Most of all, enjoy yourself :-)
Nige