A friend posted this image this morning, and it's something I think we've all heard many times over the years. But after several years of developing Lean Startup-style (even before we knew about Lean Startup), there's a very good reason to pick one over the other two.
IF you go the "Good & Cheap" route, you spend a lot of time building something. You slave away with relatively few resources over a long time to lovingly craft something of high quality. In the time that you've spent building it, the world has continued to sprint forward, and when you release your beloved project, it a.) may already be obsolete, and b.) no one may have wanted what you're building anyway.
IF you go the "Fast & Good" route, you burn money incredibly quickly. You can release something polished in a short amount of time, but you spent a huge amount of money polishing up something... again, that no one may want. In a startup with limited funds, this is also basically a sprint toward death, because once you've burned all your money, you're dead.
IF you go the "Cheap & Fast" route, you build something to test a hypothesis - do people want a particular thing? You're not building the best version of the thing, but you're building something that validates whether people want the thing you're building as cheaply and quickly as possible. When you release it, objectively it may not be "good", but if it finds an audience in its early state, then what happens is that you can spend more resources (mitigating the cheap) to make it good, knowing that you've built something that people are interested in.
You can go from "Cheap & Fast" to either of the other two by either spending more time & more money - but you can't go to "Cheap & Fast" from either of the other two.