Depends if you buy the medallion and buythe car or lease the medallion and buy the car.
Here are the numbers for buying/buying:
Medallion Payment + $925/mo car + $~1100 (insurance & expenses taxstamp, liability, GPS workers comp , renewal fees). About 6k down in this case. For handicapped cars: add about 200/mo in payment, $50 to insurance costs, and 8k downpayment for car. Works out to about 1225 for a hybrid, less for a handicapped, at current prices.
I don't know about leasing/buying, but I think that the deal is you pay about 1125/wk, which covers everything except repairs, and in three years, your payment drops the amount of the car payment per month. You then get to keep the car 2 more years since you are a long term driver.
But don't waste your time doing the lease/buy deal. Work like a dog, save up 50k, and buy the medallion and the car. Buying the car. leasing the medallion is not building any value to you, only making the leasing agent happy because some shlub (you) came along and relieved him of the hassle of maintaining a car, when all he really wants to do is lease out the medallion anyways.