I generally saved up a little nest egg before setting out and lived off that till the need to work was getting important.
At 21 I spent the entire summer traveling with my wife and living in an old Econoline van. We budgeted a certain amount for food and fuel each week and had enough cash to last 10 or 12 weeks. We traveled all over Canada and the USA that summer, with a bed in the van we could stop and sleep anywhere. We had other equipment so spent time at places like the free camp in Jasper Alberta living in a tent. Rarely did we pay for a camping site, once or twice the whole summer.
I've also hitch hiked but never "tramped" for extended periods. Hitch hiking I always had a destination.
If you want to be a "rubber tramp" I would suggest a mini van with a 4 cyl engine, or a small station wagon. Set up with bed, curtains etc. it can be quite cozy, warm and dry in bad weather and reasonable on gas. It helps to know a little about mechanics, but in lieu of knowledge get a reliable vehicle that a knowledgeable person has checked out as reliable. Then be sure to do the routine maintenance like oil changes etc.
As far as working along the way goes, most places have temporary employment agencies where you can find work a day or two at a time. There is also plenty of seasonal work in some places, like picking fruit or grapes or whatever the local economy does. If its only for a few days at a time anything is bearable if it brings in the money to eat and carry on. I found picking grapes to be quite interesting, learned a lot about vineyards. Plenty of them around here.
Do some online research about places you are interested in going and see what you can learn about seasonal jobs at those locations. Alaska for example will have fish cannery jobs during the fishing season at some coastal centers. Ski resorts hire people for the ski season, that sort of thing.
Part of the trick is to live as cheaply as possible. Don't spend foolishly on things like motels and restaurants. Learn a little about nutrition and daily requirements, nuts and dried fruit will hold you over for a few days while hiking, but you will suffer in the longer term if you don't eat a balanced diet. I once lived on fried eggs and peanut butter and jam sandwiches for quite a while when I was young and trying to be independent. I didn't know how to cook anything other than frying an egg. When TV dinners gave me food poisoning I decided to learn how to cook. I became a very good cook in time.
Another part of staying healthy is bathing and keeping your appearance reasonable. There is nothing like running into someone who hasn't bathed in many weeks. Gross! People just turn away when they see a filthy person. Its hard to find a hot shower sometimes. I see people taking sponge baths in public washrooms and I think "Good for him" and good for us too. You can always do a load or two at a laundromat and go to a public pool for a swim and a shower on the way in and out if nothing else. During warmer weather there are rivers and streams.
Where I live in British Columbia we have hundreds of forestry campsites in fairly remote wilderness areas. There are lots of remote hiking trails as well. With a reasonable vehicle you can get to some truly amazing natural places and camp for free as long as the weather holds. Most are way out on logging roads that can be traveled with two wheel drive. There are plenty of maps available and Internet resources as well. There is an interactive map of all the BC forestry sites at http://apps.gov.bc.ca/pub/recst/
I use that resource along with google maps to plan my outings and explore possibilities.
There is no greater scripture than nature, for nature is life itself.