Ensuring that you have your paperwork sorted, earnest money put away, your downpayment funds ready to go, and your real estate agent ready to write an offer as soon as you find "the one" will make the entire process go as smoothly as possible.
The first types of offers that sellers will likely reject are ones from only pre-qualified buyers for a mortgage. Pre-qualification means that a mortgage company has really just taken a glance at your financials to give you a rough estimate on what the amount and interest rate would be. (Often, pre-qualification doesn’t even involve a credit check.) In a seller’s eyes, this means that a lot of things could sink the transaction.
Instead, get a pre-approval. This is a more rigorous process that will look at your credit report, verify pay stubs, bank statements, and other financial documents. If you pass their underwriting requirements, the lender will give you the actual numbers for the loan you’ll be able to get once you find a home (and then provide you with a letter to provide as proof).
If you’re very serious about getting your dream home, you may be able to get a pre-underwriting letter. This is a more thorough process that includes a thorough examination of financials and other documentation needed for a mortgage.