Does it matter how you obtained the money you have in the bank?

Yes.  One of the considerations of the lender in determining whether or not to loan you money, is whether or not you can afford to repay the money.  Let's say that your current rent payment is $1,000 a month, and your new housing payment after you purchase the home is going to be $2,500 a month,  The lender will be looking for some proofs that you can afford to pay the $1,500 increase in monthly housing payment.

You have 10% for the downpayment to purchase the home at $350,000 ($35,000) and you have the money to pay your closing costs ($6,500) and you have the income to support the $2,500 a month ($85,000 a year) and you have little or no debt payments.  On the surface, everything looks good.  Now the lender wants to see 12 months worth of bank statements, including the statements for the account where you have the $41,500 or so that you are using for the downpayment and closing costs.

Everyone seems to know that the lender needs bank statements.  But they don't stop to think about what the lender is doing with those bank statements.  Ideally what the lender is looking for, is that you have accumulated the $41,500 or so that you are using to pay for your downpayment and closing costs on an equal monthly basis over time.  Since your new housing payment will be $2,500 and your current housing payment is $1,000, it will be obvious that you can handle the new, higher payment, if you are consistently putting $1,500 into your savings account.  If they look at your bank statements and see $1,500 transferred from your income to your savings account for over two years, and that is how the savings account grew to be $41,500, then that is proof that you can afford the new,higher payment.

If however, the bank statements show that you had no money left over every month, and the $41,500 you have in hand came in all at once last week, that is a big red flag that you really cannot afford to pay $1,500 more a month on a housing payment.

That does not mean that you cannot get a loan if the $41,500 was an inheritance or bonus.  There are many ways to get around lending standards  But whether or not you need to prove to the lender that you really DO have an extra $1,500 a month, you should prove it to yourself.  For some period of time before you purchase a home, pay your rent of $1,000 a month and put $1,500 a month into your savings account.  This will not only help with the loan process, but it will help you prove to yourself, that you are willing to live with the trade offs in your life, associated with a $2,500 a month housing payment.