You may or may not need a new bottom bracket. It depend on the crankset you choose, that determines the spindle length you need.

Example: If you choose to get a Sugino Messenger crankset it will need a 103 bottom bracket. Measure your spindle length and if it's 103 you're good to go. If not, it's only a $20-25 expense.

The bottom bracket you have, TH square taper, will serve you well. It's TH Industries. Their BBs are often rebranded, like FSA (I've heard). I have two of them and haven't had the first problem with either.