Sounds like fun! Here's my thoughts/suggestions (sorry for run-on):
3 weeks will be tight but do-able if well planned. You don't want to lose too much time by taking too many slower routes or spending too much time at layovers. If you can at all do 4 weeks, that will make a big difference. We find that overnight stops are tiring as you don't have time to set up and have to get up and go early the next day. I prefer to do some longer legs to be able to spend a couple of days at a CG. You may find the trip more enjoyable if you have the time available to be able to stop for sightseeing along the way if you come across something interesting. We are going to plan for that this year for the first time as I know we have missed out on lots of interesting stops and have regretted it.
Have been to California many times over the years via interstate and the coast. We took our TT to Reno last fall in a 3 week trip and wasn't too bad in 3 weeks but a few more days would have helped a lot. Going there, headed up to the Oregon Cascades east from Portland via hwy 26 & 97 to Klamath Falls and then through the northeast corner of Cali. - absolutely outstanding scenery. Return we went over to Redding and then the coast via hwy 299 (very twisty hwy through the mountains) and then 101 through Wa. to Port Townsend. This year we're doing another 3 week trip south and just in planning stages. Going to Monterey for a few days and then over to Vegas for 3-5 days. May come back through Nevada, Utah and Idaho via I-15 & I-84.
As you mention, suggest going I-5 in one direction and then a slower paced scenic route on the other, or a combination thereof. Everyone's different but my preference is to get there fast and take a slow trip back. I quite enjoy towing on the the I-5 and really like the run up to Grants Pass. Not a lot of CGs along I-5 in many sections though and not many RV-ers on the I-5 compared to other routes. Besides the stay at Disneyland, suggest finding a nice place somewhere to stay for 3-5 days (or longer if you take 4 weeks) where you can just relax and veg. out, like maybe on the coast somewhere. Closer to home, we like Ocean Shores in Wa.
Suggest to put the Oregon Coast aside for another time when you can take the time to thoroughly enjoy it. It will be a slow drive due to traffic and the winding and narrow roads and there is so much to see and do. Astoria isn't all that far away that you can't get there in a short time from BC. Have gone all the way to SF via 101 by car and it is spectacular and you don't want to rush it. When to get to Ca. on the 101, there is no quick and easy route back over to I-5.
You *could* go through the Or. Cascades out of Portland and then get take 97 to I-5 just north of Redding. Could take 299 to the coast then 101 to SF. San Francisco is really worth the effort to stop there and suggest trying to make it work. But do not take a trailer into SF - don't ask how I know. We stayed at a KOA in Petaluma (just north of SF) which was quite nice.
If southbound on I-5, could take 199 out of Grants Pass to the 101 in Ca. I-5 from Stockton to La is a stinking hot, straight-line drive. Interesting if you have not done it. Have not been on hwy 99 but that might be an option. The coastal route from San Jose to La is somewhat slow as I remember it but scenic of course.
There are many route options east of I-5. Check a map for hwy numbers and google them. There are some good websites with road descriptions and some with videos of the roads so you can actually see what they are like. Check for road constructions and stoppages during your trip. Also look into forest fires and be prepared to alter a route if needed.
One problem with heading down south is getting through or around Seattle. This time we are going to take the ferry to Port Townsend from Whidbey Island and then the 101 on the west side of Puget Sound. The ferry trip is wonderful and the 101 is scenic. You can back to the I-5 at Olympia. We're going to take the 101 down to Astoria and then will cut over to I-5 out of Cannon Beach. Return, will take a route through Wa. that gets us via hwy 2 to Everett so we can skirt around Seattle.
CG choices will depend on what CG membership(s) you have and can affect your route(s). We have RPI and Thousand Trails but are finding difficulty with finding CGs in some areas and will have to use a few private ones which can be pricey. If you haven't yet, try RVparkreviews.com for CG user reviews so you don't get unexpected surprises. Have heard that CGs in Ca. can be pretty busy in the summer so need to have the trip well-planned and pre-booked far enough in advance. If you don't have a CG membership, a one-year membership in Thousand Trails could more than pay for itself but you'd need a 2-zone pass. Once in a while they have a 2-zone special or you might be able to find a pre-owned one on the internet for cheap (we just got a top of the line one for cheap).
As Seamutt said, Black Bear restaurant at Mt. Shasta is worth a stop. Very cool place and area. For sightseeing suggestions and recommended CGs, that'd take up a few pages - maybe on another post.
Almost forgot, if you have a towable RV, of note is that the max. speed limit in Ca. is 55 mph on un-divided 2-lane roads and could be a factor to consider. My max. is 65, but towing at 55 is so painful. :(