allowing customer to choose one of 4 shipping methods

I would like to allow the customer to select one of four shipping methods during checkout. I have looked at simple.inc, shippingoptions.module, multiple_active_shipping_modules, and so forth, and have tried to figure out which to try by following the threads which reference them; but each attempt appears to end in "this needs more work...", so I can't figure out which to use, nor how.

Is there some reliable way to enable the customer to select one of several shipping methods, each with a flat rate, at checkout time?

TIA