You can offer more than the asking price, as long as the property will appraise. Build in Seller Contribution to be applied to your closing cost. On FHA and USDA loans you can get up to 6% of the sales price applied towards your closing cost. In most instances, you can get in for little or no money. These are legitimate mortgage programs , designed for low to moderate income families.
Add 4% to the Asking price and ask for 6% Seller Contribution. Be careful not to ask for too much, because you can only apply real cost , don't leave money on the table. A good Lender can calculate how much money you will need to get from the Seller. firstname.lastname@example.org
Congrats on cleaning up your credit though. You are on the right track.