Take a look at pathchar if you want a tool to estimate the characteristics of different network links between two sites. Having said that, I believe that "random" sites you might select to probe may view your attempts as hostile and respond with complaints to your upstream provider(s), counterattacks, modify the results that you get, and otherwise interfere with your project.
Also, you've got no good way to know (without asking) if the host/network in question is going to be injured or inconvenienced by your efforts - either because they don't have a flat-rate connection, and/or because they actually need the bandwidth they pay for, and subsidizing your "research" isn't something they've agreed to do.
In sum, I don't think your idea is a good one, and I don't think you'll learn very much from the effort, other than that other people don't like it when you screw around with their networks for no good reason. If you really want to know about the characteristics of network connections, you can probably find this in discussions occuring at a business/budgetary level for providers or consumers. If you really want to play around with measuring network characteristics, that's cool, but get permission first or do it on hardware that you legitimately control. Don't just arbitrarily bother other people on the Internet.