As someone who used to run, cycle and swim a lot, I've picked up injuries from all three at some point or another.....and most of those injuries were my own fault for not listening to my body and pushing on regardless.
Approached correctly, starting to run can increase bone density and help strengthen your legs in general. However, if you try and rush your results, push beyond the level your body is ready for...that is where you can pick up injuries, not just in the joints, but with ligaments and muscles as well.
Start with run/walk/run, until you find you can run without needing to walk. Then, as others have posted here, don't increase your distance by more than 10% in one go. Also, learn to think of rest as part of your training plan. Running every day will keep your body in a fatigued state, slow down your progress and increase your chance of injury.
In terms of technique, if you can hear your feet slap/slap/slapping on the floor as you run, then that means a lot of shock is travelling up your legs and into your knees. Hitting the ground heel first is not good, it should be towards the toe. Try and run so your foot strike is almost silent.
Finally, if you decide running is for you, then I'd really recommend getting some good advice on running shoes from a local independent sport store. They know their stuff, will assess how you run and provide the right shoes for the job by doing something called 'gait analysis'. We don't all run the same way. Decent shoes are much cheaper than physio and far less painful than a sprained something or other.
Enjoy...