Hello and welcome. All that running does get a bit monotonous. With a bike you can travel and see places. It sounds like you don't want to spend too much. Might be an idea to start off with a second hand machine to test the waters. For little money you could get a vintage drop bar bike, trouble is unless you know what you are looking at you can get a load of trouble,
@biggs682 of this parish has some which are fully checked. What's your height?
As for clothing all you need is some shorts and a top, plus some shoes which clip into special pedals but you can just use ordinary foot ware for starters. I think Aldi, or is it Lidl have cycling gear for cheap. Someone on here can advise. Don't forget a basic tool kit, a pump (floor type) and picture repair stuff. Good luck.