Being able to ride for almost an hour is pretty good. As others have intimated, don't worry about speed - your speed will trend up as you ride more often. Instead, focus on time in the saddle and exploring places you wouldn't have gone if you were in a car.
Other hints:
- Take regular breaks when riding. There is no prize for having the sorest arse.
- As mentioned, get some 'bar ends' which allow you to change hand positions as you ride, which should help with neck pain. There are other adjustments you can make to the handlebars (position or change to a different shape) that might help if the pain doesn't gradually get better as you ride more. Even rotating the bar in it's clamp or changing to a different type of grips can make a difference.
- Keep your tires well inflated (if riding on hard packed surfaces, a 115 kg rider should keep their tires pumped up around 50psi or more - more will roll a bit faster, but with transmit more road shock to your body; lower pressure will be more comfortable but requires more energy to keep the bike rolling, and if you go too low you can get pinch flats.
- Finally, 'reward' yourself for riding - go to an ice cream shop in the next town or grab a pint at a pub or take a relaxing rest next to a burbling creek - and after a while the riding itself will be more of a reward. My favourite reward I only earn once per season or less - my reward for riding so much that I wear out my tires is new tires!