I've been using FlashGet for years. It incorporates with Firefox, IE, not certain about Opera, Safari, or Chrome.
It allows me to establish preset destinations, but also to change destination on the fly. It also keeps a database of what files went where.
You'd have to add the FlashGot extension to Firefox, but that's fairly simple, low memory footprint.
One thing of which you should be aware - depending upon how it is configured, it will also add a text file for each download with the same name as the download, which I like, but that is easily adjusted in the configuration.
Might give it a look. Low learning curve, loads automatically, pretty much a no-brainer to use. Couple of extra clicks, but well worth it for the value it provides.
[Edit: I don't like the dialog extenders because they tend to be too limiting, but they do work.]
