This is just a short list of some of my favorite Lightgun games and the systems that they are available on. Its by no means a complete list but its the core set of games that I wanted to get up and running.
If you are interested then there are plenty of instructions on getting the necessary emulators set up on this site and this list can just form a checklist for you.
I almost always just default to the most modern console that I can emulate well for any even game if there are multiple options.
The Wii and the PS2 are probably by 2 best recommendations for getting started as they are quite straight forward. I have to recommend the PSX as well just for Point Blank (my favorite!) though.
Here is the list in text in case that helps:
|Dead Space Extraction|
|HOTD Scarlet Dawn|
|Point Blank 1|
|Point Blank 2|
|Point Blank 3|
|Resident Evil: The Darkside Chronicles|
|Resident Evil: The Umbrella Chronicles|
|Time Crisis 2|
|Time Crisis 3|
|Time Crisis 4|
|Time Crisis 5|
|Time Crisis Project Titan|
|Time Crisis Razing Storm|
|Virtua Cop 2|
|Virtua Cop 3|