Bit late on this thread.
I pulled my old mtb out of the shed last Spring and started the long road to cycling fitness. Like you I found the first few rides really hard - 10 miles had me properly blowing. After a while I swopped my knobbly tyres for slicks, which made it a bit easier. As for distance, I was finding 50 miles about my limit in terms of comfort. I then bought a road bike - nothing fancy, a £600 Cararra, which has done great service. My average speed increased by a whole 3 mph, but I've peaked at 15mph and don't see myself going much quicker. I can now comfortably ride up to 100 miles though, which is what is important to me.
Regardless of your bike, the main way to improve is riding the miles, the more you ride the easier it gets. Some times you have good days, sometimes the ride does not work. Luckily, the great thing about cycling is that there is always the next ride, which in your head will always be the best ride !