I plan on walking as my primary mode of transportation. And I’d like to stay for at least a month, so I might be staying longer.

The reason I asked about access to a vehicle while you are here is that, if you are dependent on public transportation and catching rides to get you to the trailheads, then your ability to move around within Oregon will be limited once you arrive here. For example, you mentioned an interest in both the ocean and the mountains. Public carriers, like Greyhound, are usually limited to getting you from one town to another, and few trails start right in or near towns with bus service.

On the other hand, if you have a vehicle, you'll be able to transport yourself to any part of the state, be able to access both trailheads and campgrounds with ease, could get supplies with no trouble, and could see a much wider variety of places. For example, you could spend a week at the coast, two weeks in the Cascades and another week in the extremely beautiful Wallowa Mountains in NE Oregon.

There is a Pacific Coast Trail, which is more of a route than a continuous trail. You must hike the beach portions with attention to high and low tides; it routes you inland in many places to cross rivers via highway bridges, because they are very big rivers and cannot safely be crossed in any other way. It shifts often between trails and road-walking. This route has the advantage of frequently accessing small towns where you can get supplies, but camping is limited and motels are frequently a better bet. The coastline in Oregon is, however, spectacular almost everywhere you can go.

The Cascade mountains are about 100 miles inland from the coast and there are no trails I am aware of to get you from one to the other.

A typical possibility for a month-long hike in the Cascades, without a vehicle, would be to take a bus from Portland down to Ashland, Oregon. There you could fairly easily hook up with the Pacific Crest Trail and walk the length of the state (about 430 trail miles!) back up to the Columbia River at Cascade Locks.

However, this would be an exceptionally challenging backpack for someone with your tiny amount of experience and I wouldn't recommend it without extensive preparations that you most likely do not have time for. Among other things, you might well run into plenty of snow in the mountains next July, covering the trails and making both hiking and navigation quite difficult. Not a novice-friendly hike!

Edit: I strongly agree with OregonMouse that August would be your best month to hike here, as the choicest parts of the state can be covered with snow until late July. Or later.