Get a map of the area it is pretty simple once you get going. You are not allowed on Expressways so you have to follow along the Lower Roads. Signs are a bit confusing so try and work out the route before you get there. Out of Bangkok Roads and Highways are great around Thailand, beautiful riding. Hope you get up to Chiang Mai.
You can't go around BKK (yet) south of the city. To avoid (too much) traffic I suggest generally 4 to Nakhon Pathom, 323 to Kanchanaburi, 324 to Suphan Buri, 329/33 to Nakhon Nayok, 33 to Pratchinburi, 3077? through Khao Yai Nat park etc.
You can find all the small roads on your own map to avoid the main roads and to be able to relax and take in where you are rather than concentrate on everyone else. . Ie 3394 from Ban Pong to 3356 to 3260 to Suphan Buri etc....