The question should really be broken up. The first part of the question is with regards to gifting. How much can parents gift children without any tax implications. I believe the amount is 11k per parent to each child or spouse thereof but CONSULT WITH YOUR CPA.
Now with regards to the home. If you want the home to be held in your name only you want to get the money seasoned. Thus have it in your accounts a few months prior to wanting to obtain the loan. Different lenders have different seasoning requirements but if you go to get the loan and 24 days ago there is a whopper of a deposit into your account that aint gonna fly. So having the funds in your account a few months will save you a hassle later. Otherwise you may want to simply consider having your parents in the loan with you. Of course they will be obligated to provide the lender the same amount of info you will need to provide but it may be an alternative for you to consider.