Obsidian

I've done a few. A webhost certainly helps, if money's an issue you can start by checking out free hosting services - most of which rely on advertising to pay the bills and might upset your carefully crafted page layout. It's also worth checking if your internet service plan includes a webspace allocation (could be anywhere from 10 to 50 megabytes) and what conditions are attached to its usage. Self-hosting is an option if you have a static IP and a reasonably fast connection, but it's not for the fainthearted. A fourth option is to have your pages hosted as a subdomain on someone else's site.

As for uploading - that's traditionally done with a FTP client, though whoever hosts your site might also support browser-based uploading.

Have you tested your website with a non-Microsoft browser to see if there are any compatibility issues?

I've always been lazy and uploaded through the windows shell. Never bothered with an FTP client. If it's a Doom site and relatively small-ish I can probably host it. I can't recall how many ftp accounts I have spare, but I'm sure I can delete an old one that's not being used if need be. PM or email if you're interested.