The 62.5 is cheaper than 50 micron but not as cheap as 9micron singlemode. Problem with singlmode is the cost of electronics and connectors. If under 500 feet 62.5 will be all you ever need.
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Go with 62.5 multimode with sc connectors. I would just do a couple of gig media converters and use whatever switch you want.
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You are better off with the 5e for HDMI. Should be no need for Plenum either. Unless your house and or shop use the attic space for the AC return air. If its duct you are fine with PVC.
I would just go cat 5e. Cat 6 is a over kill for sure, as you can run a gig over 5e. just run a drop from your router to a second wireless router in the shop and you will be good to go.