The Oregon coast is a pretty fantastic stretch of coastline, complete with a ton of off-bike adventures and amenities to make the whole thing enjoyable. Late September/Early October would be a nice time–after the summer rush, but before the weather really starts to get inhospitable to long days of pedaling.
I’ll say right off I had a hard time finding info on a company that just offers gear shuttling for a ride like yours. There are certainly many companies that offer guided, supported trips, but as far as a shuttle service, this was the only one I found. It comes highly recommended.
For lodging, you’ll do best to look at your route first, estimate your daily mileage, and focus your searching on the towns you want to stay in. It’s worth looking at VRBO.com to see if there are some smaller, private rentals that might be available, since that’s always a nice way to go, but can also be impractical for single night stays.
Here are some recommendations for coast lodging, dining, and things to see/do.
From an overall planning point of view, here are a few great links you might find helpful:
Oregon Department of Transportation (ODOT) Bike Routes (note the link to Oregon Coast Bike Route)
Great Oregon rides around the state (be sure to look at the resource links)