As far as maps go. While I did ride it with paper maps + the Bicycling the Pacific Coast book on my first trip in 1998 - I did have some tricky sections including (a) getting out/,through Vancouver, San Francisco and LA bypass. Your Rand McNally maps just won't have the details and you would likely have to augment.

My suggestions; for the Oregon section, the State bike map is fine, similarly for northern CA it is also fine. However:

1) If you go with maps, the Adventure Cycling maps are worth it. They will get you a better route including several more tricky sections across Vancouver, San Francisco and Los Angeles.
2) The book is dated but otherwise could be OK resource but I would favor the maps.
3) While I've had a bike computer as an odometer for most all my touring - I more recently experimented as a navigation device. Having at least distance is helpful on navigation on paper maps. Having a device note turn by turn points can be a handy thing you get used to but also not strictly necessary in my opinion
4) I would struggle some with only the Rand McNally state maps (and I've done the coast multiple times in different trips)
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