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Id stay away from the Feather if your new to this style of shaving. But as Mark said, a mild razor paired with a non-mild blade does work well.

What you have is concidered the New Style gellette...

As TC said.
There are many to choose from. You're looking for D.E. (Double Edge) Blades.

The issue you will have after finding the 100's of name brands made now will be to find what works best...