Essentially - at the beginning all you need is a nice straight runway (And for that matter, its not all that different from a highway). Taxiways to get aircraft in or out of the runway(s), and a hut somewhere to seat people. 2 runways would be a good minimum (one in and one out) I'd say 4 would be sane - heathrow had 6 back in the day, and struggles with 2 nowdays
Large covered garages for storing vehicles or aircraft maintenance would be awesome.
Aerobridges are nice, but many aircraft can be boarded through internal steps or a mobile staircase.
While traditionally ATC's a tower, many airports have large towers as a 'showpiece'. Radars are often regional, but having a small 'local' radar would be useful. These are not that large - military radars are often vehicle mounted.
London's main airport, heathrow's actually a pretty bad example. They have trouble getting an additional runway approved for example.
Terminals are all about people processing. A minimal, people processing terminal is no different from a regional bus station. Luggage is a problem - you need to get it in and to the right plane and the right way. Then of course, customs and immigration, holding people to and boarding. Assume enough capacity for one average airplane in each stage and you're good. Add some space cause people would not be happy being treated like cattle.