For me, it's been roughly 50% apartments, 50% extended stay hotels (whether it's a hotel or a bed-and-breakfast-type place). In all instances, though, I was invited to visit for work or I applied for a temporary position, and the contacts/connections to get me lodged and ready to roll were built into the invitation/application.
Hence, I'd focus on the work angle first and let the accommodation/transportation angle sort itself out. That's assuming you're serious about working abroad. If there's a job out there for you, I'm sure the people who will be employing you will be happy to help you out.
I do this less now that I've got a kid, but working abroad for a month or so at a time is a ton of fun. You get a nice slice of living and have enough time to settle in and assume new routines, do new things, so on. I guess it assumes a certain attitude, but if you've got the right mindset it's a great way to get by.