Can you pin the favorites center in Firefox like you can with IE?

Try the “Smart Bookmarks Bar” add-on. That might do what you’re looking for.

One of these should definitely work for you—

View -> Sidebar -> Bookmarks
(if you want access to ALL your bookmarks. You can organize your bookmarks into folders, and use a quick search box at the top of this pane to filter your bookmarks.)

View -> Toolbar -> Bookmarks Toolbar
(if you want most frequently used bookmarks to appear as icons on your toolbar, you can use this. You decide what links appear here and in which order.)

[Off Topic] The ‘Xmarks’ plugin for firefox helps me keep my firefox bookmarks in sync across my personal laptop and my work laptop.

Hope this helps.