Like anything, it depends on where you're starting from. If you're in your twenties or thirties and in decent shape, sure, kettlebells are great. Probably not so much if you're an overweight middle aged man with back problems.
I run about 1500 miles a year, plenty of people in my running club in their sixties and seventies who're in great health. Loads of studies showing that running is good for you long-term. I think if you have an existing problem with ankles, knees etc. from some other sport, then it might not be so good. If you look at the hundreds of thousands of people who run 5k at parkrun on Saturday mornings, only a small minority are "good at running".
Burpees , on the other hand, would injure me very quickly I suspect.
In Niels's case, I'd do the exercises saint1 suggests. Achilles tendinosis is one of those things that definitely responds to eccentric heel drops and so on and it only takes a few weeks. There's been several sports science studies showing they work, Hakan Alfredsen is the guy who originally showed this. I would be a bit wary about doing much running until any pre-existing condition definitely sorted out. Obviously you need to keep doing the exercises even when it feels better. If it was a sprained ankle rather than achilles, I'd be doing exercises for that as well. Once you've sprained your ankle once, you're at a higher risk of doing it again.