You can examine the whole route on Google streetview. WSDOT also has many webcams along the route, but no traffic maps until you get close to Tacoma.
I suspect WA3 from the Hood Canal bridge to Poulsbo will feel heaviest, especially in the morning, since it is 2 lane. South of there it is mostly divided highway. Rush hour traffic into Tacoma is bound to be heavy, though I haven't experienced it myself.
101 to Olympia is a long way around, with a long stretch of waterfront driving (scenic, but curvy). And then there's the I5 drive back to Tacoma.