Yes, start gently. 3km is less than 2 miles.
And don't push yourself, don't use pacing tapes or Apps. Just gently plod along. I use it as an opportunity to explore - where does that footpath go? what is down this road? ..........oh look, there is a lovely pub I didn't know about. I will come back and visit that. Etc.
Invest in a good pair of
proper running trainers from a specialist outlet; they will still cost much less than a gym enrolment.
I know keen cyclists who have got pot bellies, so although cycling and swimming might possibly improve heart-lung efficiency, it won't necessarily help get the weight off or improve the body shape. Also, cycling is dangerous and a pain in traffic and over drains and pot-holes, and swimming requires more logistics than jogging, where you just get up and go from your front door.