Quoting Laleh.
How many kilometers should I be looking at?
Rather than just looking at kilometers, consider balancing that with the quality of the vehicle and its individual history. For example:
Quality - Some engines and drivetrains simply last longer than others - kilometers-wise - even among the same makes and models. Some models had a great couple of years, meaning the manufacturer put in quality parts that all worked together in concert, making a very reliable overall vehicle. The next year, the manufacturer used a different series of moving parts here or there and it wasn't as reliable as the previous model(s). In short, some makes/models and their moving parts have good and bad years. If you're geeky enough, find reviews from industry experts regarding the make/model/year of the powertrain - the engine and transmission - of whatever vehicle you have eyes on; plenty of this information is online. Numerous consumer reports are also found online - these highlight trends regarding mechanical problems with a specific model-year and its associated moving parts. Or, make this all easier by asking your mechanic; ask if they've worked on that particular model of engine and/or transmission and see what they have to say about it. Will they tell you it's good, or tell you to run far away from it? 
History - Some used vehicles have been driven foolishly and haven't been well-maintained and other used vehicles have been babied, either by the owner, a mechanic or both. If it's a private sale, ask a lot of questions to the owner of the vehicle like how long they've owned it, what work has been done to it, was it ever wrecked or rebuilt and - this is important - why they're getting rid of it. Has it become suddenly possessed by evil spirits intent on making it a doom-ridden heap of junk?
Look at the whole picture, not just numbers on the odometer. 
Having said that, purchasing a vehicle with, say, 400.000 km is something best left to those who are serious about vehicles, like mechanics, hobbyists looking to restore a vehicle, collectors, etc.. Find a nice balance of those three: quality, history and kilometers. 
I bought a van with 100.000 mi (160.000 km); the model-year of this van was far superior to the previous model-year, simply due to the transmission the manufacturer put in. I used this van for 15 years as my day-to-day vehicle at home and it was a champ. After that we hit the road, lived in it and traveled internationally with it for over two years. I bought a quality used vehicle at the time, one with good guts and high mileage. I sold it while we were on the road quite easily; the buyer knew - by the model and its year - that it was still a great van aside from all the miles and use we put it through over the years.
Quoting Laleh.
Can I buy one with a 15k budget?
You mention travel in Australia; I'll assume you'll be buying there, with AUD?
I don't know about the market for campervans there - I can only guess. There are loads of other forums and groups dealing with campervans/schoolies/vanlifers specific to that country which will give you a much better idea of how far your budget will go. Many of these forums and groups have marketplaces where members are selling their vehicles.
Again, I can only guess what your budget gets you in Australia - an older vehicle, perhaps 15 years or older with high kilometers. It might need some work to get some or all of the living quarters working properly, in addition to any engine/body work. There's the issue of class, or size of the van, and the overall condition of it (see History above).
Quoting Laleh.
Any specific and important hint for inspecting a campervan?
Again, consider your mechanic if you have one. If you aren't too comfy with inspecting it yourself, ask your mechanic to come along in order to see a prospective campervan with you.
Your mechanic would look at the following and if you're comfortable with inspecting it yourself, look out for these too - many are the same things to look out for with almost any used vehicle.
1.) Puddles of fluids, like oil, and coolant under the engine/transmission. Do this before and after test-driving it and while the engine is running.
2.) Check the condition of engine hoses and belts - they should be supple and not dried or cracked.
3.) Look at the tires - is there uneven wear on one side? This indicates a bunch of problems with the steering and/or and suspension system. These may or may not be serious problems.
4.) Start the engine, step outside the vehicle and listen - do you hear clicking, whining, scratching noises? These can indicate a host of issues, like a bad bearing in a pulley or emission system sensors going bad, or a hundred other things. Of course, engines make all sorts of noises - some indicate problems, most don't. While you're there, look under the engine while its running (see #1).
5.) Flip all the switches on the dashboard and make sure each function works. This goes for anything in the living quarters too. Does the bed fold-away? Well, fold it up and pull it out - several times. Make sure all of this stuff easily works. If so equipped, make sure everything in the kitchen is clean and properly functioning.
6.) Does it have an awning? Unfurl it and look for rips and tears. Look at the exterior of the van for major or minor cosmetic damage. Are there hook-up spots or connections - are they in good nick?
7.) Look underneath the vehicle again - do you see any rust? If so, is it just superficial? Do you see any holes that have been filled and patched-over?
8.) Look for water damage inside the vehicle - all sorts of holes have been drilled and cut-outs made into the van in order to kit it out and sometimes these may develop leaks through the years. Having said that, does the van have a musty smell? Sometimes that water damage isn't so visible as it leaks down into the floor; if its carpeted it can smell musty.
9.) Ask yourself how it feels to drive it? Is it nimble? Does starting the engine make you feel like you've just unleashed a panther ready to pounce? (
) Or does it feel unwieldy? Is it this big noisy mess that barely rumbles down the road?
Good luck on your search - and have a blast on the road! 
