Hi there,
I have an Olympian M27 Frank Hayes model mitt from the late ‘30 that looks similar to yours. For cleaning, I would use some saddle soap and give it a good scrub; I like Fiebing’s. For conditioning, I like to use Horseman’s One Step on leather like this; it should soften it up and give it a nice display worthy conditioning and shine. For the buckle, I would use some fine no. 0000 steel wool to get rid of the rust. After that, a wadding metal polish like Nevr-Dull to shine it up. Hope this helps.
Here's a pic of my mitt:
It was the first vintage catcher's mitt I ever bought and I like the marbling of the leather on the front. It's a medium size mid-line model but I’m still quite fond of it.