The LED strips that are available very cheaply these days make ideal and beautiful lighting for display cabinets. They're very easy to install and run off low voltage so there's no danger of shock.
Here's a display cabinet that we've had for over 20 years. It's a nice piece of antique furniture and has a lot of cool stuff in it, but it is quite dark.
I bought a 5 meter roll of this LED strip. Non-waterproof, with connectors. I got warm white, I prefer something around 3000K or a bit lower.
First I plugged the strip in and held it inside to decide how I wanted to place it. Then I cut the strips to length (there are locations marked where you can cut and solder wires on to run power to the next strip), and soldered wires between the strips. A "3rd hand" clamp as shown here helps a lot.
I cut some strips of wood and spray painted them black, then hot glued them to the bottom of the shelves to block direct light from the LEDs which would be ugly. Finally, I peeled the release paper off the back of the strips, exposing the sticky surface and put them in place, one below each strip.
I used a 12 volt, 2 amp "wall wart" power supply - I have a box of the things, they come with external hard drives of which I have quite a few and I only ever use one or two of them at a time. I drilled a hole in the bottom corner of the back of the cabinet to admit the power cord.
Here's the result: