Need guidance and advice for a mixing valve
If your existing shower is a two handle type (independently controlled hot and cold) the simplest solution would be to install a temperature actuated flow reducer. This devise can be added inline between the shower head and the shower arm. It will reduce the flow out of the shower head as the temperature gets too hot. This will give you time to adjust the temperature before getting scalded.

The best solution is to replace the existing shower valve with a modern pressure balanced one. This type of valve will adjust the flow of the hot if there is a drop in pressure on the cold side due to a toilet being flushed. This would require you to open up the wall in order to replace the valve (easy if the back side of the shower wall is accessible).

Update: Some manufactures sell a cover plate for converting two (or three) handle shower valves to pressure balanced ones. The cover plate conceals the leftover holes in the tile from the old valve. Here's a clip from Ask This Old House on installing one.

If you’re not able to replace the valve, but the water lines are accessible (in an attic or basement), you could install a point-of-use thermoplastic mixing valve on the hot line that feeds the shower valve.

You can also adjust the temperature of your hot water tank, however you don't want to set it too low as you would increase the risk of pathogens.

Lastly, adding check valves will not help if the issue is pressure balance.