Verizon and US Cellular are the dominant carriers here, with stores around to sign up and buy a phone.
You should expect to lose cell service when you go hiking or travel far from Arcata and other local towns. The mountains routinely block cell signals. If coverage in these areas is important, you can install Signal Spy on an Android phone to see which signals are being received at your present location, and their strength. The app is probably only useful if you already have cell service, are experiencing problems, and are researching a carrier to switch to.
Verizon is probably your best bet, unless you want Project Fi.
Project Fi works here, but the initial website check that asks for a zip code (post code) tells people the region is not serviced. Local people sign up by giving the website a zip code for an area that is serviced, just to bypass the initial check. Some people experience problems activating their phones and have to call Google's customer service to get going. While your existing phone might work with Fi, unless it's an authorized "works with Fi" phone, it won't identify the strongest carrier signal and switch to it automatically as you travel around the region.
Fi's pricing plans are designed for people who don't use much data. If you are concerned about 4G speeds, you probably use a lot of data and should avoid Project Fi.