I like fire FTP's integration with firefox and it works wonderfully with my X10 account, my Comcast account, and numerous other accounts with no problems. It can store many profiles at once and changing between them is a one click operation. I haven't used any other software extensively besides this, but I believe it is fully featured, intuitive, and has a simple drag and drop GUI.
When I'm editing my sites, I usually use the built in thing by Dreamweaver, or this plugin for Wordpress that allows FTP access. When I'm not using either of those, I'm probably using FireZilla, which is the probably best way to go for the Linux techies.
core ftp lite and filezilla are both very good, it's just a matter of personal preference, filezilla is slightly easier to use, but core ftp puts the advanced features right there in front of you.
I have a really old one called WS ftp pro, it actually works very well, despite the fact that it looks ancient. I would suggest that you use filezilla through. Remember also that code editors such as dreamweaver and notepad++ have their won inbuilt ftp clients.