No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
When you find home which you like it and its in your range you can send sign purchase contract to your lender. The lender will ask for current documents and start the process of mortgage. Which generally take 30 days to close.
The lender will walk you through the process when you will be ready.
Add to the list:
1. Homeowners insurance
2. Letter of explanation for deposits and withdrawls from your bank account that can not be explained by direct deposits from your employer, tax refunds, etc
3. Letter of explanation for credit situations (this is broad but happens)
4. If your down payment is coming from a different source that is not your bank account which they already have a statement, you'll need to provide a LOX for that too
5. LOX for gift funds (if there are any)
That's about it, IF you don't have any credit situations.
What's the lender?