3 weeks is down-right leisurely
As Michael said, this gives you plenty of time and you should have no problem with taking breaks as needed for the baby while still seeing a lot of things along the way.
There's no one best route as it all depends on what you want to see. I suggest getting out a big map of the US and start marking national parks and other places you want to see. A logical route should start jumping out at you.
After you've made a few decisions on places to visit, please come on back here, share your information, and let us help you by giving you some recommendations of other things to see along the way, tweaking routes, etc. Happy planning.