tortoise - don't worry about cooking meat.
In fact when you buy fresh, packed meat at most stores they give you a guide as to how long to cook. Also you can test things like whether a whole chicken has cooked in the oven or not. A good test is stick skewer or fork into the breast and the crease where the thighs join the breast, if the juice runs clear (i.e no signs of pinky or bloody juice) it has cooked.
With other things like pieces of lamb or beaf, fry some onion in oil first, then add the chopped meat (small pieces obviously cook faster) and then cover the meat with water or stock, it should cook properly within 1 - 1.5 hours on a low flame. You can also taste the meat while cooking, if it is nice and tender to bite, not hard and chewy it has cooked ! You can then add you veg. or whatever at the end to avoid over cooking the veg.
Mince meat cooks really quickly, again fry onion, add meat, add water or stock or tomato paste, etc, cover with water and lower heat and allow to cook for about 20 mins.
I am really paranoid about uncooked meat too as I have had food poisening in the past from badly cooked, or gone off meat (not my own cooking, restaurant food !), but with a bit of practice and common sense it's dead easy to cook meat safely.
Good luck !