There are specialized electrical switches that mount into the door jamb or against the closed door. These work similar to the light switch in a refrigerator. Since moving on to LED strip lighting and magnetic switches I have not installed a mechanical door lighting switch in years.

They are still available, I suppose.

Regarding the light source, there has been an explosion in LED lighting. Not only economical cost but they exist in a huge variety of forms. The type I find myself using most often is the LED strip light. A flexible but sturdy tape with LED emitters mounted every so many mm apart, these strips can be cut to the desired lengths and the backing is self adhesive. Very easy to install.

If you want to enclose the LED strip for appearances, extruded aluminum sections are available for mostest cost. Being aluminum they can be cut using hand tools or even a carefully wielded shop saw. I favor the angled profile with white diffuser cover (style 007 in the link).

LED strips are designated based on the type of LED chip used and the density, number of LED per foot or per meter. I find the 5630 (each LED chip is 5.6 X 3.0 mm) type to provide useful brightness. The strips I buy consume 4.5 watts per foot, 300 LED per 5 meter spool.

The most common LED strips run on 12 volt DC power. The power supply is a typical wall wart style or laptop style power brick, depending on how much power is required to run all the lights.

There are dimmers available, including remote control dimmers.

In my view LED strip lighting has superseded fluorescent tube lighting, CFL spiral lamps, halogen pot lamps and pucks. Especially where space is constrained or heat is an issue, such as an enclosed cabinet.