If you have no outside obligations, there is absolutely no reason to stay in a low-mobility job you dislike, and anyone who tells you different is just trying to justify their own stagnancy. If you like to travel, make it happen. And I have found that traveling is refreshing- it won’t turn you into a different person, but it can give you a hell of a lot of perspective and shake you out of bad pattern.
That said, I would strongly consider looking into Peace Corps or other similar service. The advantages are:
It can advance your career and put you into an amazing professional network- it’s a really smart career move.
You’ll get a deeper and more fulfilling experience than you would just passing through. And, you’ll still have plenty of time to travel.
You’ll probably learn a new language.
Outside of costs to complete the medical clearance forms, you won’t have to pay for it, and will even come home a little ahead.
You might do some good in the world.
Lots of people meet their spouse in Peace Corps!
It is a long process, a big commitment, and not for everyone. If you just want to be footloose for a while, that’s fine, too. Thousands of people do it, and I’ve never heard anyone say they regret it.
Some advice:
Think cheap. You can live easily in India and China on $10 a day. In Europe, that may not get you lunch. Your money will last longer and you’ll have more freedom if you stick to affordable countries. $10,000 sounds like more than enough to me for cheapish countries, especially if you are willing to spend a month here or a month there in one place. Make sure to think about things like visa costs, etc. Hostels and food can be cheap, but there can be a lot of little expenses you might not have considered. There are all kinds of “travel around the world” guidebooks that will have better advice.
Have an exit plan. You can bum around Asia indefinitely picking up English and bar jobs (yes, this is realistic in Asia), but you’ve only got so much time in your life to do that if you don’t want to end up being that scuzzy old guy at the shady English school who’ll never have a real life. Have fun for a while, but don’t teach English for more than a few years unless that is your only goal in life.
I wouldn’t worry about the car unless I was in some very specific regions (like parts of Africa.) Most places have good public transportation and it’s the best way to meet local people.
Choose quality over quantity. A longer amount of time in a smaller number of places makes for better travel than just quickly flitting through the world. If it were me, I’d focus on four or five countries and spend some real time in each of them, maybe connecting them with a cool overland trip like the trans-Siberian railway. I’ve seen long-term travelers get into ruts where everything ends up repetitive and superficial, and it tends to turn them into pretty boring, obnoxious people. Watch out for that. But other than an idea of what countries you are interested in, I wouldn’t bother planning more than that.
Finally- keep money for your own plane ticket home, and for goodness sake, nobody wants to read your autobiography. Nobody wants to read another boring travel memoir. If you are serious about writing a book, you’ll need to approach it like a journalist with a compelling topic, lots of research beforehand, connecting with people you’ll interview and places you’ll go beforehand, etc. You aren’t going to write a book that sells just bumming around.