When USCIS approves your work authorization, you may receive a Social Security number from your local Social Security office. You should get a Social Security number immediately, even if you do not plan to work. Your Social Security number will allow you to establish a joint bank account with your US citizen spouse, and place other assets like investments in both of your names. Your Social Security number will also make is easier to put your name on any lease or deed regarding your marital residence, and on the title to any vehicles you and your spouse own.
USCIS considers joint ownership of assets to be an important indicator of the genuineness of a marriage. The more joint assets and responsibilities you can show, the better off you will be at your adjustment interview.