First Time trying to Get a Apartment on our own EDIT

Hey Ladies! So me and my SO are planning on getting a place together by Fall. We are 20 and 21. We have saved up around 11k which is all in my account (We do not have a joint account and we are not married). We make pretty good income at around 4k monthly together. My credit Score is at green score at 735 and my so hasnt really started his credit. Meaning he has one credit card for Kay Jewelers and thats all. Im wondering do you think we will get approved? What do they check. We have the money we worked hard for and will my credit score be good enough if he doesnt have much credit? We are clean no troubles with the law ever. Any advice? Thank you in advance!