Questions regarding shoes

New guy here, couple of quick questions.

After hopping onto the fixie craze, I’ve caught the bug as it were, and I’m keen to head down to the velodrome. However, I lack any form of proper clothing/apparel. I’ve managed to pick up an NJS build on a whim for a decent price, however I’m just curious as to the “proper” type of shoe/cleat that should be used with it? Pedals are MKS Royal Nuevos.

Any help would be greatly appreciated.

Keep the mks for around town and buy some cheap shimano/look road pedals and some road shoes
No one has used mks style cleat/pedal combo in 20 years.

Or if you have size 6 feet, keep an eye out for the Asics Keirin shoes.

I think a good pair of shimano would be perfect for you and won’t break your bank.