For a hobby that mostly involves a lot of walking, golf requires a player to exert themselves in amongst the gentle stroll with dynamic moves which stretch, twist and pull your muscles in different directions that they are not used to going in.
Back in 2010 I had tight hamstrings and needed a specific program designed for me that not only increased my flexibility, but also allowed me to cope with the stress of playing 36 holes in one day. I needed to get fitter, leaner, stronger and more flexible. Here is a copy of the program that was designed for me:
The amount of time you spend exercising will largely depend on the time you have available and your resources. I think too it is important to appreciate your limitations. I would 100% recommend visiting a qualified fitness instructor and if they have a good idea of how the body moves in relation to the golf swing then that is even better.