It sounds like you probably have a bit of osteoarthritis, which is age - related changes in the joints that make then stiff and sore, especially after exercise or other strenuous activity.
At the same time weight loss
is really important for keeping yourself healthy over the long haul. Therefore, trying to find exercises that you can perform that do not hurt your joints (so that you can keep performing them) is important.
I suggest that you think about lower impact exercises. Running and jogging are probably too high of impact for you, but swimming, elliptical, or even just walking might be tolerable. The recommendation for healthy living and weight loss is that you engage in at least 30-60 minutes of aerobic exercise most days of the week. The exercise has to be sufficiently vigorous to make you sweat and raise your heart rate. So you should look for a type of exercise that you can perform at this level without being too sore.
Luckily there is no magic about one type of exercise versus another. So, pick which ever form of aerobic exercise is most comfortable for you. If you can perform that exercise at the recommended level, then this should help you lose weight.
Don't forget to talk with your primary care doctor
before initiating any exercise program, just to make sure there are no medical reasons why you would need to modify your routine.