Soldier Class Decision?

Random. This is why its a good idea to cycle your rookies in and out to see what class they are. Plus sometimes on your adbuction missions a reward will be a high ranked class.

My experience has been the same -- it seems to be random, though some rookies do seem to tend toward their future classes.

As for the bit about forcing you to let three guys die...? Disable the Tutorial before your next new game.

That is the tutorial part. You can turn that off. When you start a new game goto advanced options and click the checkbox off Tutorial part. It will take you right into a mission that you have full control with. You don't get that first satellite for completing a Council mission but get to keep your first 4 guys.

It appears to be random. You can only be sure of getting one of each out of the first four.
Starting stats are the same for all rookies, and class determines their aim score, increasing a set amount each rank. Only the will score is variable, and it doesn't correlate to class or 'The Gift' as far as I can tell.

It really is completely random. An example of why is that once you unlock the "New Guy" perk, then every single recruit you get is automatically assigned a class even if you haven't used them, this includes past and future recruits. It's annoying yeah. When I got that particular perk, all the recruits I had became nothing but snipers and heavies. Had to recruit more to get other classes.

Totally random. I just started a new game, I have more female Heavies than male. I do seem to see more male soldiers than female overall though. It took a second play through and hiring a stack of new soldiers right at the beginning to get a 5 woman team (I took the first squad expansion ASAP) for the achievement.

The class a recruit gets is randomly selected once you finish a mission where said recruit has earned a promotion. So if you want a recruit to get a specific class simply use save/load to finish the last turn of the mission until your recruit gets the class you want him/her to get.

Obviously won't work in ironman mode though

It is 100% random, and I mean 100% random. Not a single character is pre determined in their class. This means you can even reload your save and an individual soldiers class will be different the next time. I tested this for a fact while playing the first mission. I made sure each soldier killed an enemy and saved before I took the last shot. I completed the mission, was not satisfied with the outcome, reloaded, took the same shot, and got completely different classes. I did this as many times as it took to get the soldiers the classes I wanted them to be. Likewise you can also do this when starting the game if you are not satisfied with your starting soldiers as well as any soldiers you hire. Again it is 100% random so use and abuse saves to get the results you prefer.

Super totally random. I'm pretty far into my current game... bought the new guy perk, so new recruits get auto promoted to squaddie and are assigned a class.... I hire 2 rookies at a time, and abuse save reload to get whatever I want. (btw, will gain is random too). Save JUST before they arrive, and load if it's not how you want. Doesn't work for iron man of course.