So, what are the most common types of camping sites I am going to come across while crossing the country? Are parks with a fee the most common or are small campsites the most common?
Of course I will be stealth camping along the way also, but what will I be running into most along the way in terms of types of camping and prices?
I'm trying to get an idea of what I might be encountering. Mind you, my budget is not the loosest, so price will be a high priority when looking.
Ideally I would like to camp in places where there are others camping, but where I won't be spending $20 a night.
Depends on what you're looking for. If cost is a big concern, then you'll probably tend to avoid the higher-priced camping. Some people are willing to pay for camping in exchange for nice showers, a picnic table, a leveled tent pad, a convenient store and a higher level of security. But if you are very price-sensitive, you'll be willing to compromise on these things. There's a whole range of stealth camping. Sometimes you're pretty sure that you're not suppose to be there, so you take measures to not be noticed. Other times, you think it's okay to be there, but you're not entirely sure. So you risk being rousted in the middle of the night in order to save money.
I avoid most commercial campgrounds, which tend to be higher in cost and lower in ambiance. National Park campgrounds are usually higher in cost (unless they have hiker/biker sites), but are typically worth it to be able to stay in a really cool place. National Forest campgrounds are usually less expensive, and sometimes free, but typically have fewer amenities. City parks are often my favorite, since you can usually camp there with permission from the police (and thus feel somewhat safe from being rousted), usually have bathrooms, and are within convenient reach of the service you need.
Bottom line is that it depends on what you're looking for. If you take two different touring cyclists traveling the same route, one of them might be camping free every night and one might be spending $20 to camp every night.
Of course, there are many other inexpensive or free alternatives to camping, such as Warm Showers, Couch Surfing, churches, fire stations, hostels, etc.