I've always shot service rifle or used glass for 'any rifle any sights' long-range stuff, so I know little to nothing about match rifle irons.

What sort of base do I need to mount the rear sight at the back of the rail?
What sort of base do I need to mount the front sight to the rail on the gas block?
Any suggestions for sources on parts, or specific parts?

Thank you

There are rail mounted rear sights.  As for fronts, I usually see them clamped to the barrel.

That is for the fancy space guns.

Depending on what you want to do/spend, Champions Choice has a good selection of adapters and sights:

http://www.champchoice.com/store/Main.aspx?p=ItemDetailOptions&item=CCM3LR  can be used with a Lyman 90MJT.  I use it to mount my Redfield Palma.

http://www.champchoice.com/store/Main.aspx?p=ItemDetailOptions&item=CCAR1050  is good with a Lyman 93

They also stock the Centra sights if you want to go with a direct mount.

Champions Choice and Champion Shooters Supply are good sources to start with.

Also Creedmore Sports,,

https://www.creedmoorsports.com/product/LIPSKI-CRSBASE/sights-and-sight-accessories

https://www.creedmoorsports.com/category/creedmoor?utm_source=googleads&gclid=CjwKCAjwtuLrBRAlEiwAPVcZBl08Pg8ZXI4T0ejoJwoKepagwXrseIfz4WRrWqt3ihwWVcEAEKWwIRoCMyMQAvD_BwE

OK Weber, also
White Oak Armament
White Oak Precision