It's not much about being on a budget or not, FFMPEG does the job well (a lot of softwares and scripts are based on ffmpeg), the thing is, it's open source, so you're not gonna get any kind of support and there is no pretty interface, it's a command line tool.
If you have some money to spend on this (FFMPEG is free) you could just google "FLV encoder" and see what your options are. Personally, I've only used ffmpeg so I can't recommend any other software.
If you expect a lot of traffics on your website, you should also look at flash servers to stream your content.
Hope that helps
