Start by making your 4 lanes roads, build neighborhoods insides the quadrants like I did above and connect it directly to your highway. Then, once you start making money, you'll be able to easily incorporate the missing road layers into the mix.
Using road layers is the best way I've found to control traffic so far in my city building career. Here's how it works, keep in mind this city has no public transport. Everything is flexible and works as long as it stays within it's own road layer. It's also important to avoid making too many exits inside your populated areas. I usually make 4 connections, one on each sides of my area. I hope this made sense to anyone.