I've trained with both these. I prefer RMI. The NOLS courses are available through REI. In my opinion, RMI adopts more up-to-date techniques and draws on lessons learned from the GWOT while NOLS/WMI tends to appeal to the tree hugger crowd. In my opinion the basic first aid classes offered by Red Cross and the like are basically useless.
The WFA (wilderness first aid) class can be done in a weekend and provides a good grounding in emergency medicine. Both organizations use the same language and protocols for training from first aid through ALS. I think the minimum class they start to teach tourniquet use is wilderness first responder, which is about a week long class.
My certs are expired now, but last training I had emphasized aggressive bleeding control and treatment for shock. Once that blood has left the body it cannot be replaced outside a trauma center; BP can be supported temporarily with fluids but the best course of action is preserving as much blood volume as possible.
https://www.remotemedical.com/
http://www.nols.edu/wmi/?gclid=Cj0KEQjw2ua8BRDeusOkl5qth4QBEiQA8BpQcEEgiEb0XE1pgrQLHgSFHQCGtIHKebX_4kzBy5DiywYaAvCR8P8HAQ
I don't have any direct experience, but Insights offers a class including trauma care and I'm confident they would be more geared toward shooters.
ETA: good on ya for seeking training. Each item in there has a skill set associated with it. Having said that, if the tools are available and I am bleeding out, don't stand there waiting for instruction. Try what you have available, to the best of your abilities.