What you'll want to do is get Wordpress to push the post to LJ. LJ as far as I know doesn't have the power to pull data in from somewhere else. (And most cross posting systems prefer to push data out than pull data in anyways.)
So - you'll want a plugin for Wordpress to send the stuff to LJ, and set your configurations in Wordpress to tell it where you find your LJ. You may want to take a look at this one: http://lj-xp.com/
If it is a wordpress powered blog, lj-xp is a wordpress plugin that will automatically crosspost entries from your own wordpress blog to your livejournal (or your account on another lj-powered site). I would imagine there are similar plugins for other popular blogging platforms. AFAIK, only syndicated accounts will directly post from a feed on lj's end.
Now that I think about it, you're right about wordpress.com. ljxp was widely recommended for people looking for alternatives back when lj started cracking down on various fandoms a while ago. While you can install the wordpress(.org) software on pretty much any sort of shared hosting service, that's a big can of worms to open when all you want to do is just write. I know there are quite a few lj clients that can post to multiple services, but I don't know of any that support crossposting.
WordPress is really quite easy to install and configure now, and doesn't require a dedicated server; just a hosting account that supports php/mysql. You can get totally inexpensive hosting at a place like Dreamhost and auto-install WordPress through their web panel.
It's more complicated than just running a blog at wordpress.com, of course, but you get a ton more flexibility.
Feel free to drop me a line at email@example.com if you want some further explanation.