Since I'm not a huge fan of any of the current solutions for managing the resources and knowledge that I have, I was thinking about making my own solution, which will involve custom code as well as possible integration of FOSS solutions. I would start development on my local machine, but if I like it, how difficult would it be to migrate over to a public server and let others also use this tool? What kinds of challenges might I be facing?
In theory, nothing, beyond just the process of moving stuff to the new machine. You can set up your own servers, on your own ports (port 80 for example).
You can even create your own fake domain at home, with just a tweak to the /etc/hosts files (or the equivalent on Windows).
Now, if you're developing on Windows and hosting on unix, you'll have platform issues, so I'd suggest against that, at least for a first project.
But other than that, it should be straightforward.
You didn't hard code any paths to "localhost" did you? If so, that should be the first thing to strip out. Either use relative paths, or have a configurable {AppPath} variable of some kind that you only need ever change once.
By the way, what language/framework are you using? it would help us provide sample code.
I would add that documentation is a highly important factor in any project if it is to be quickly embraced by the public. The tendency when developing in-house projects, especially if they are just for your own personal use, is to neglect, or even completely ignore documentation of all kinds, both of usage, as well as in the code. If users aren't told how to use the product, they wont use it, and if other potential developers don't know how or why things are done the way they are, or what the purpose of things are, they either won't bother with trying, or will cause other problems unintentionally.