You can get a re-entry permit for any entry stamp if you want to. But it doesn't do anything except prevent your permission to stay in Thailand from being cancelled when you leave Thailand. It won't add any extra time or anything.
If you're asking if the 1 year multiple-entry non-O visa based on marriage is still available, the answer to that is no. The only non-O visa currently is the 90 day single entry non-O visa.
It's likely the instructions from the embassy say to print the visa and hand it over with your passport. For Thailand, you always want everything printed. You probably could get in without it printed, but you would need to make sure the passport control officers understands you have it because there's a risk of you being stamped in incorrectly without it. You'll still need it printed later anyways for your extension and possibly for your bank.
Generally Kasikorn or SCB due to the increased transfer limits from Wise to those banks. Bangkok Bank also has an increased transfer limit but that bank is best to be avoided for now.
In the end though, it's whatever bank will actually let you open an account that is the best one.