Buy a bike today! Unless it's really hot out, then wait a week. An average hybrid will be ok, except for that rear wheel, and it will tell you when/if it breaks. Basically anything tougher than a full-on road racing bike will do you fine.
DO NOT WORRY about speed. The speed on different kinds of bikes can vary a lot and just getting used to riding brings it way up. The speed on an exercise bike is a fake number. You can turn down the resistance and pedal like hell and get whatever you want. You can probably get a power number out of your exercise bike... it's not really calibrated but it will be a good thing to watch. If you don't have power, use heart rate. The people who do serious training have power meters built into their cranks and they use it along with their GPS.
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Genesis 49:16-17