Different figure painters use different techniques for displaying their miniatures. This will depend a lot on whether you have to transport them or not.
If you wargame with them and often do so elsewhere, you may not wish to unload your miniatures on a display case at all. One methood of transporting miniatures unharmed is to purchase a pistol case, one with the eggcrate foam. The indentations between each foam section will fit a figure nicely. They will not bounce around or bump into each other, thus protecting the paint on them.
Another way to keep the figures from bumping together is to purchase a multicelled box like the type that crafters use to organize embordry floss in. You can pad each cell or even better, you can glue washers to the bases of your miniatures and then purchase sheet magnets, which you can cut up into squares to fit the cell where the miniature is to sit. This will keep them rock solid if a good quality magnetic sheet is used and the washers used are iron/steel based.
An actual display cabinet is very nice for showing off figures, especially those that are not meant for gaming so much as to just display your favorite pieces. You can purchase what are known as shadow boxes from craft stores. These are wooden boxes separated into cells that hang on the wall as a formal display. Often craft stores will sell small shelves to show off miniatures and small knick-nacks. These work as well. You can always have one custom made to your specifications as well, though this is the most expensive option.
The main considerations for storing and displaying your miniatures is keeping dust off and keeping the miniature from bumping other hard surfaces, which will chip the paint off. Any solution which can fit these needs should work nicely.
I don't sell anything on this site, and I provide all information free of charge, so if this site has helped you, please consider donating to help support adding more content to this site. Just click on the Tip Jar image above.
If everyone pitches in just a few dollars/Euros, I can add videos and more tutorials to serve you even better.