You want to start searching for a family Dr ONCE you get a OHIP card. That is how Doctors get paid, no OHIP card, no payment from the ministry. You can look around, but as mentioned, they want that card. Every time you go into your Dr office they will swipe that card, every time you go into a walk in clinic, ANYTIME you have contact with a office providing medical care, they want to see that card. If you do not have the card, then you pay. If you want to continually just go into a walk in clinic forever, then No, you won't need a family Dr, but for continuity of care I would recommend trying to find one
And just keep in mind, not all family Dr's are accepting new patients, some are totally full. So you gotta do your leg work in trying to find one. Once you get your OHIP card, you can go to the Ministry's website and there is a site there that you can put in your information to try to find you a family Dr. .
I am not saying all walk in clinics are all bad, there are actually a few great ones in Toronto when I cannot see my family Dr fast. But you build a relationship with your family Dr, they will get to know your history.