If you want to see the United States and understand what makes it what it is, you must get out of the cities and do some cross-country travel. And the only practical method of cross-country travel in the US is by automobile. The good news is that everything is organized to make automobile travel convenient. All the roads are built to accomodate vehicles larger than anything you are likely to be driving and you will always be able to find food, lodging and fuel along the main routes.
The passenger rail service in the US is called Amtrak. The trains are roomy and comfortable and, if you have the time, they offer a much more civilized means of getting around from city to city than airplanes do. There are a couple of drawbacks however. Amtrak does not actually own most of the track it runs on. This track is owned by various freight lines which means that if there is a scheduling confilct, freight takes precedence over passengers. In practice this means that delays are more likely than not. The other problem is that there are many places Amtrak does not go. You cannot go to Las Vegas via rail for instance. European visitors should be wary of two things when contemplating a rail trip in the US. First, Amtrak will happily sell you a ticket to places with no rail service. In these cases they will get you as close as they can by rail and put you on a bus for the rest of the trip. Second, I have seen offers in European travel publications for rail travel packages to places where I know there is no train service. There are numerous short haul excursion trains around the US. These are often called "dinner trains" and they use abandoned or little-used rail lines for entertaining two or three hour round trips. The Mt Hood Railroad and the Sumpter Valley Railroad are two Oregon examples. These can be entertaining and a good value for what they are but they are not a way of traveling anywhere. I have seen some tours advertise a package of these excursion trains worded to sound as if they were offering a rail tour when they are not: they are offering a bus tour with rail junkets at selected stops. Caveat Emptor.
When I was young, bus travel was common. Now it has virtually disappeared as a long-haul method of travel. A patchwork of local services remain here and there but as far as touring the US by bus goes, the best I can offer you is "Good luck."
I see lots of Recreational Vehicle packages. These sound attractive: go where you want, stop when you want and you have everything you need without the cost of motels and restaurants. There are two problems with this. First the economics are not that good. A comfortable car that will carry a family and a reasonable amount of luggage should get around 8liter/100km. A typical RV will get around 24liters/100km. In Oregon in 2012 gasoline costs around $1.11/liter. If you travelaround 300km/day, the car will cost $26 per day in gas and the RV will cost around $80. Add up fuel, milage charges and base rent and a motel can be cheaper. The second problem is, while it is nice to have everything with you when you get there, it means you have to lug it all around with you. Secondary roads that are no problem for a passenger car can be difficult in an RV. RVs can work if you are planning to stay a few days in each stop and stick to the interstate highways but for a journey of exporation, a car is better.
I go by car. A standard passenger car gives the maximum freedom to explore. If it is a county road or better (i.e. if it is on a map), a modern car with all season tires will be able to travel it in summer season without difficulty. I try not to drive more than two hours without a break. Oregon highways have many rest stops, historical markers, interpretive centers and viewpoints all along their highway system. They are there for you and you should take advantage of them. I have found that the slower I go, the more interesting the journey is. If you are traveling in the eastern parts of Oregon, it is a good idea to never pass a gas station with less that half a tank. You never know how far it might be to the next one.I stay in motels. I usually do not bother with reservations. The US is built for traveling and there is always a motel when I need one. Prices vary with location and amenities but mostly run from $50 to $150 night. Usually I decide where I am going to stop for the night around 6 or 7 pm. If it is an unfamiliar town, I will drive through town to the other side to see what my choices are and then turn back and go to whatever seems the best. The only time when you will need reservations are on the big travel holidays: Memorial Day at the end of May, 4th of July and Labor Day at the beginning of September. The only other times you might have trouble finding a room would be local celebrations. Portland during the Rose Festival, Pendleton during the Roundup, Eugene during Commencement. Worst case, you may have to drive a little bit longer but l have never needed to go more than forty minutes past my planned stop.
If I see something interesting, I change my plans, it is the secret gardens and the hidden treasures that are the most valuable.
Oregon is full of mountains and the temperature and even the weather can change radically with altitude. It can be a nice day in Portland and a full blizzard on Mt Hood less than fifty miles to the west. From mid-June to the end of August, the chances of snow or ice on any Oregon highway is very small but it is always a good idea to check on conditions before starting out. The Oregon Department of Transportation maintains a travel advisory web site
which gives information about current road conditions everywhere in the state. Oregon plows its major roads and winter here is less severe than it is in many places so if you are used to winter driving you should not have any problems. Studded tires are legal in Oregon from Nov 1 to March 31 and my experience is that studded snow tires and four-wheel drive will handle the worst Oregon is capable of without fuss.If you do not have deer where you live, let me give you some advice: deer are cute and lovable suicidal idiots. The favorite deer trick is to stand at the side of the road looking at you as you drive by and, at the last possible instant, leap in front of your vehicle. This usually kills the deer and does several thousand dollars worth of damage to your car. Also much of Oregon is grazing land for horses and cattle. While most of it is fenced, some is not, and fences can fall down allowing livestock onto the road. One popular breed is the black angus which is flat black all over and at night almost invisible on an asphalt highway. At night always watch for eyes at the side of the road reflecting your headlights and act accordingly.