Do people tend to stick with similar topics? Is it easy/difficult to explore new areas? (Or is it all funding-dependent?)

A similar question was asked just the other day. See http://www.postgraduateforum.com/thread-34236/

In the future you should expect to stay in the same field but you'll have flexibility with topics. For example if your PhD is in Economics don't expect to become a sociologist later in life but you could venture from International Economics for example to Labour or Development Economics. That's what I'm doing right now.

In many of the social sciences your PhD topic tends to be your workhorse for quite some time, meaning you want to get a few strong articles out of it, and beyond that, you can take unexplored corners of your research and get a fellowship / post-doc out of it...while still publishing as you chug along.

If you are intent on becoming an academic, that first lectureship usually depends on how hard you make your PhD work for you post viva regarding publications and post-doc work. If non-academic / applied research is your aim, you can usually drop your PhD main interest like a hot potato upon getting that cozy UN / Consultant job.