I'm not gonna be useful for the police/criminal side of this, but I can certainly help out a bit on the medical side - having been in the ER for several gunshot wounds (well, not me myself personally being shot, but treating patients and stuff).
In the case of a non-fatal gunshot wound (say, in the thigh or shoulder), what would the ambulance officers do on the way to the hospital?
So, EMS's main job is to stabilize the patient in the field - and keep him stable on the way to the hospital. They'd be mainly concerned with staunching the blood flow from the wound - so lots of pressure to the injury site. They don't usually use tourniquets anymore - we don't like them in the ED. They cause too much of their own tissue damage.
Then, like a lot of other people said, monitoring the patient - pulse, respiratory rate, heart monitor, oxygen saturation. The ABCs of resuscitation are airway, breathing and circulation - if the patient is awake and talking to you - not so many worries about the first 2, but if they're bleeding, obviously gonna worry about circulation. If they're unconcious, and we don't know what other injuries they may have, they automatically get a C-spine collar and placed on a back-board. The ambulance guys will be calling ahead to the hospital to let the trauma team know what's coming in and the extent of injuries. They're also gonna want to keep track of the amount of blood loss (as much as they can).
IV will definitely be started - that's the first thing we learned on our trauma surgery rotation - 2 large bore IVs, 2 Liters of Normal Saline - STAT. <g>
Also, would the fact that it's a non-super powered Kryptonian play a role in the surgery?
Surgery's gonna depend on where they are shot and the extent of damage. Having never dealt with a non-human patient (<g>), I can't speak from firsthand experience. But abdominal wounds are gonna get exploratory surgery no matter what. If it's an extremity (arm or leg) wound, it'll depend - a straight through shot with no evidence of hitting the bone or EXCESSIVE bleeding is just gonna get stitched up and watched (although sometimes not even stitched - higher risk of infection).
I don't know how much difference Kryptonian physiology will make - unless we're dealing with organ damamge - probably going to have things in different places. May bleed differently, etc... And definitely no transfusions, which could be really bad with a gun shot wound if he's bleeding. He'll definitely need a lot of other fluid resuscitation then - IV fluids (normal saline, lactated ringers, etc.)
Also, where would be a good place to shoot a normal person? In the stomach? What would happen if you shot someone in the stomach? What kind of surgery would that involve? How long, roughly, would it take?
No real good place to be shot, obviously.
If you mean good, as in not gonna cause all that much damage, then arm/shoulder or leg. Nice big chunky area with muscles and easy to clamp-off blood vessels. It'll be a little trickier if it hits a MAJOR blood vessel or bone, but still better than chest or belly.
Stomach is generally NOT a good place to get shot. There are way too many organs and blood vessels that can be damaged. Even a straight through shot gets emergency exploratory surgery because we don't know what else might have been hit. There are good odds that the bowel will be damaged with a gunshot wound - and depending on the extent of the damage, at least some of the bowel will need to be removed - so pretty decent surgery. Liver injuries are BAD - they bleed like stink! Spleen also bleeds like stink but you can remove that if you need to. Liver you have to try to keep - we need that.
A simple exploratory surgery (for the belly), with no internal damage will probably take 1-2 hours, depending on anesthesia, etc. IF there is damage, it will take LONGER - bowel resection 2-4 hours, depending on how much they have to take out. Liver/pancreas/kidney/other solid organs - again will depend on damage, but probably a decent amount longer 3-8 hours.
That was a long post, I could have gone longer.
Let me know if you need any other specifics.
Jill