I am with the "just pull on some trainers and run" brigade (although "proper" well-fitting trainers are of course a good idea in the medium to long term).
I am not really a fan of running tbh and haven't run much for about 5 yrs (since training for an adventure race) but I started up again a few weeks ago, pulled on my 10 yr old Ron Hills, 5 year old road trainers and hit the muddy footpaths in the Chiltern hills on my doorstep. I suspect my technique was terrible, I was definitely in the "wrong" shoes and I ran too far (about 45 mins) but guess what, it was great and I survived.
Will I get properly fitting, off-road shoes at some point, yes. But for now I am just happy to be doing some exercise.