PC needs to have an Internet connection, video processor (with appropriate outputs) and CPU capable of doing the job. What is appropriate video and CPU depends on what is the target display, SD or HD, and what inputs it has.
I stream HD OK with Intel i5 dual core and Intel HD graphics, daughter does it on AMD dual core with AMD 2400 graphics.. I have other PCs that can't do the job, Pentium 4 with NVidia graphics, Celeron with pre-HD Intel graphics.
If you have to upgrade a PC, consider that a Roku box (or other branded competitor) will do the whole job for less than the cost of upgrading an older PC to stream video. Even a cheapl BluRay player may cost less than a graphics card doing HD video.
No way you are going to surf and stream HD video on the same PC. Even with four or six CPU cores, and the fastest video processors available, there will be bottlenecks somewhere, e.g. sharing the processing of the network stream, and focus ( video app usually has to freeze for you to communicate with your browser).
I surf while streaming Netflix on the PC by using another device like IPad or a second PC. Unless bandwidth is very good, either surfing will be slow or your streaming video will degrade quality to the smaller available stream.
I've never been able to stream satisfactorily anywhere I've RVed, except my own driveway, whether I'm trying to use a MiFi I bring along, or campground WiFi. Places I choose to camp are well outside the realm of 3G/4G wireless, far from any cable or DSL. If I can't buy the bandwidth, neither can the campground. If your RVing is about parking in the metro areas of our 20 largest cities, you can probably do a lot better, you'll just pay wireless prices for the data you use.