Yeah Valtain ones are good but it's an after market one from Japan. Just a standard high 70 amp one will do you (as per picture of the one in my Mini), they were fitted as standard to the Japan cars (A/C ones).
Only thing I'm not sure of for yours is whether whoever put the Valtain one on also put new/different connectors on the loom. Can't really tell from your pics and if you bought a standard alternator you might have to change the connections too...
If you're on Facebook then you could join Classic Minis Japan New & Used Parts or JDM Classic Mini Owners Club, a guy called David Ainley runs the first one and is part of the 2nd one, he can probably advise more and/or get you a Valtain one if you wanted one.