For most mini fridges, it comes down to personal preference on storage capacity and shelf layout. Adjustable shelving gives more options.
Do you need a freezer in your mini fridge? Are you really planning to keep frozen food and make ice? If not, don't pay for this unneeded feature or waste space. (If you do need it, look for a unit with a full width freezer inside.)
Do you need a lock on it? Some mini fridges come with a built-in lock - perfect for dorm rooms and fending away pesky roommates. (You can also add a lock feature later.)
Are you keeping food in your mini fridge? If so, you want a mini fridge with a compressor to keep food at safe temperatures. Fridges with thermoelectric cooling and heating are best used for simply storing beverages.