I'm offering on a private party, off market deal

[Sam Rust]

I'm putting in an offer on a house in Greeley CO that is off-market, but that I know the owner has expressed interest in selling. I've spoken with the owner, and they were receptive to an offer and are hoping to save on realtor fees (as am I). If they accept my offer, what steps do I need to take to "lock" the transaction down? If I write up a contract stating the purchase price, appraisal/financing/inspection contingencies, and time line and we both sign, is that sufficient? 

Thanks!