If you sign up for a prepaid plan, you can order a SIM card from T-Mobile's website, activate the SIM card online yourself and set up EasyPay to automatically pay with your credit card each month.
If you want postpaid service for a single line, T-Mobile does a credit check. There are Simple Choice No Credit Check plans, but they are advertised for families only. Single lines are guided toward prepaid service if the customer doesn't want a credit check. You may be able to call in to see if you can get a single line with no credit check, but I don't know if you will be successful.
As far as the price of prepaid phones, do you have a specific example where the same phone is cheaper for prepaid customers than it is for postpaid customers at T-Mobile? There were some older phones in the past where this may have been the case, but I don't know of this situation for newer phones. Depending on the prepaid plan that you have, the phone may cost more, not less, for a prepaid customer.