Employment history (aka reportable income)
Lenders all look at debt-to-income ratio. Let’s say the bank wants less than 45% (and give-or-take, that is about right), then they want your monthly payments (think credit cards, student loans, car payments) to be 45% or less than your recurring monthly income. You don’t necessarily need to have 2+ years of employment history. Some people just get out of college and get an employer letter stating their salary in the same field as their degree, for instance. That usually works!
Your credit score greatly affects the loan types and interest rates you will qualify for. The higher the rate (ideally north of 700+), the more options and the lower the interest rate you will have. There are some loan programs for people with limited credit history (think 580-620 range), such as FHA loans, which are built to help you still qualify for a home loan. Keep in mind – the bank will take any credit score of the income being qualified for the loan. If you and a spouse are buying, they’ll look at both scores. If you have a co-signer, their score will need to be good enough. If your score isn’t high enough, but a co-signer’s score is, the lender would very likely require all of the debt-to-income ratio to be supported by the co-signer’s (aka the person who has the satisfactory credit score) income only.
Down payment/closing cost funds
Different loan programs have different requirements for down payments. Some go as low as 0%. A lot are 3-5%. FHA, USDA, VA, and conventional loans. In addition to the loan’s down payment requirement, you’ll have to consider closing costs. For simplicity’s sake, let’s say those average 3% of the purchase price. You will either need that in cash, have a gift from family (and a gift letter saying you don’t have to pay it back), or you can ask the seller to cover that 3% by increasing the purchase price proportionately.