Take the BRC and go from there. If your finances are not in line to buy a bike, I suggest waiting until they are rather than play random juggling games. But take BRC to get it under your belt so you know what yu're getting into as far as riding goes.
You'll only be frustrated and feel rushed if you try this bike rental thing to cram rides into time. Besides, what you spend on rentals could actually go into your savings pot for a bike you want.
Or you could just sell the HDTV
