Ah Matty ! You made me laugh. Most of us do not realise what a wreck of a physical state we are in until we try to improve our fitness. I didn't. Do not get me wrong, I am not mocking - I am the same weight as yourself, but aged 57, with BMI = 29.99 ! So you have all the advantages, I detect.
A lot of sense has already been posted so I will not repeat it. However, perhaps mainly for the benefit (?) of others of not quite such tender years as yourself, I append my own experience.
I started jogging about 5 years ago after a physical rest of some thirty (30) years and it was hard, man ! Coughing ? I felt so awful at first I thought I was dying !
I still do not get out as often as I should - perhaps twice a week - but can now jog 5km without dying - or coughing. My GP says don't; my AME says do. However, the latter signs the Class 1 ...
I do feel better for it and I have watched a steady if unspectacular improvement in my blood pressure. Heavens knows what my weight/BP would be if I did not jog ! I have tried swimming but I get bored doing lengths up and down. I used to cycle a lot in my youth but it is becoming, frankly, dangerous these days, with manic GTi drivers howling round country lanes. So I take to the woods nearby to run and am usually accompanied by my wife. As she is junior to me in age, height and, especially, weight, I usually have something to chase !
I would suggest perseverance, taking it comparatively easy at first and try not to have a layoff or you will surely slip backwards, surprisingly quickly; the older, the quicker. Go accompanied if you can. Avoid dark/dusk or you will surely injure yourself; I did. Keep records of your performance so that you can quantify progress. It takes a while but eventually you will actually look forward to it .....