The best approach by far is to clean it up in Photoshop first, then vectorize. You could putz around in your vector application for hours, but it's incredibly tedious and you'll still have the problem of way too many anchor points.
Scan at the highest resolution you have available, bring into Photoshop and clean up all the rough edges, random spots, etc. Save this.
From this point, there are some optional retouching tricks that may help.
To smooth things a bit more, go to the Channels panel and create a new channel by dragging any of R, G or B to the New Channel icon at the bottom. Apply a slight Gaussian blur to this channel -- enough to see but not enough to make it fuzzy -- then use Filter > Other > Maximum (or Minimum, whichever works best). You want to keep a very slight amount of blur on the edges, to avoid aliasing.
Invert the channel and Ctrl/Cmd-Click to make it a selection, then click the RGB icon to make the regular layer active. Create a new layer and fill the selection with black. Pick any of the selection tools and use the "Refine Edge" command to make any further edge enhancements.
When you have the character looking exactly the way you want it, save it and use this file in Illustrator as your base for vectorizing.
As DA01 wisely points out: do lots of testing with your font editing program.