No matter the case....unless your credit is so wrecked you can't rent something...I would avoid non-qualifying lease purchases.
I hope this answers your question. Good luck with your home search.
Incidentally, I've seldom run into lease-purchases that say "no credit check." Usually, it's "no bank qualifying," or similar. But virtually all the sellers (either the owners or investors doing lease-options) require credit checks. Now, the credit requirements may be far more lenient--especially if you're coming in with a large option fee--but in most cases the goal eventually is to sell you the house. And that means that you've got to be in a position to clean up your credit and qualify for a purchase during the period of the option.
Hope that helps.