It's a very economical way to get to experience the authentic local culture and life style in the place you are interested.
Couchsurfing is a good one as well for budget travelling, just be more careful if you are a girl, look through the host profiles in details, check out the reviews to get more info about the host. Usually, host could offer you some good idea about the nice spots in the place where are quite worth visiting.
There are also volunteer abroad programs and all sorts of other options. I highly recommend this website for finding out more: http://www.transitionsabroad.com/
firstly, traveling abroad is something you should do for yourself and not because you want to impress recruiters. Just the travel on its own doesn't impress anyone unless you've been invested in a cause or project that matters either for the job you're planning to apply (i.e. internship).
Firstly decide where you want to go, what you want to see. As i presume you're a woman, be aware that some places might not the most recommended to travel by yourself, so security is one important part which you should consider.
Secondly - a budget is not an issue. Check out for instance an "around the world" ticket that allows you to visit all continents in a certain amount of time. Try to outline the places you want to go to and find job opportunities depending on your age and qualification, so you can finance your local expenses and cost of living.
Assure you have the basics: flight ticket from home and back, a passport that's valid for more than 6 months from your departure onwards, jobbing agreements for a few places ahead of time, some money on the bank for emergency use only (i.e. emergency credit card from your parents), visas needed for the specific countries, laws are different everywhere)