For the purposes of a purchase the bank will want to have an appraisal to ensure that the value of the home meets or exceeds your contract price. Further, depending on your loan type they may have other qualifications. For FHA loans all systems must be in working order and they will want repairs made to any items such as chipping or peeling paint. They also look for safety issues. VA operates under the same guidelines. The house must be livable as is and must have a stove.
I rank them in order of importance.
1. Credit scores (from a lender not FREE sites)
2. Income- W-2 or self employeed? Part time job etc.
3. Assets-how much, where is it, did anyone give you money, any unexplained deposits etc.
That will get you started, there is more after you get pre-approved and have a contract to buy a home.
Hope this helps and please let me know if you need more information.