homie do not buy an exercise bike. either buy a real bike, or run outside. running outside will get your cardio and metabolism up way higher than any treadmill exercise bike you can buy.
all you need at home is a bench, which you can incline and decline with that special part that allows you to do leg lifts etc etc and a pull up bar.
rings? unless you're going to be doing muscle ups i wouldnt buy rings, id invest in a strong bar to do pullups on, just a regular metal bar you can anchor to something.
id get a speed rope, to do jump rope with and practice to get down double unders.
so bench metal bar and speed rope should run you something around 300$ with the weights. i think 200 pounds worth. you might also want to get a 45 pound bar and not the little tiny ones that come with the bench. and maybe another bar to do preacher curls with.
this is me assuming you're going to be doing traditional free weight exercises