In relation to maintaining the health of the microbiome:

a) Are there certain foods that should be avoided?
b) Which foods are especially beneficial?

Some tips to support your gut microbiota and hence your immune system:
Prebiotics are good foods/ vegetables that feed the microbes in your gut. Probiotics are those products that introduce beneficial bacteria to your gut. Postbiotics are those chemicals produced by microbes, that are beneficial to our body and immune system.
Fermented foods, such as sauerkraut, kimchi, kombucha, miso contain helpful probiotics, which feed the bacteria and microbes that you want to encourage to flourish.
Foods that are rich in a variety of fibre will promote the good microbes ie vegetables and fruits in general. Leeks, artichokes, onions, cabbage, chicory are richer in inulin than other vegetables - a particularly good soluble fibre to take. It can be bought as a supplement also.
Colourful fruits and vegetables such as blueberries, beetroot, blood oranges, nuts and seeds are rich in polyphenols which are beneficial to your gut microbes. Green leafy vegetables keep inflammation in check, and should be regularly consumed
Non- fermented dairy products, and meats are not as good for your gut microbiome, and should be consumed in moderation, however what is termed ultra-high processed food, really must be avoided. These foods are unnatural, highly refined, bleached, deoderised, hydrogenated and synthetic. They are a concoction of chemicals that contain no real nutrients. We ought to stick to foods that are as near as possible to their natural state.