Should I be able to escape unscathed?

Deaths should be rare. On average you should lose less than one soldier between supply drops, or things can get tough in the long run. I have found the ideal roster to have three of each class, and you should cycle them to gain even experience for them so that if your Major grenadier gets wounded, the next best one should be Captain or at least Lieutenant.

Having more than 3 per class makes training them to Colonel rank too slow, and having just two per class is too risky because a pair of same class soldiers can easily be wounded at the same time.

In the first few missions you should consider taking a rookie with the rest of the folks even if you have 4 non-rookies available for the mission, just so you have more than 4 squaddies or better to maximize the chance to avoid having rookies in the first retaliation mission. But when GTS starts producing squaddies, you no longer should need to take rookies to missions.

When the average rank among your troops is at least somewhere between Corporal and Sergeant, try to buy replacement soldiers from resistance HQ or Black Market instead recruiting a rookie when you lose one, because they will have sufficiently high rank and this won't set you back your plans to get as many Colonels as possible. Sometimes you might have to wait for a supply drop or two until the correct class becomes available.

Getting multiple soldiers wounded constantly is also bad. You should have a flawless mission every now and then, and on average only have 1-2 soldiers wounded per mission, so you can always have enough battle-ready soldiers. Use engineer in AWC when necessary, or consider even using the HQ scanning bonus that makes healing faster in dire situations. Usually there is a few days wait between missions so you have a window to heal for a bit.

You should not be losing soldiers. XCOM 2 is much stricter on this than XCOM 1 and the older X-Com games. In X-Com, troops were definitely disposable.

The reason is that there's no room to train your troops. Tough aliens come at you fast, and the Avatar counter forces your hand. High level troops are vital to survival, more so than good equipment. The game tracks the number of corporals you have and how early you get them - that's how important they are. You simply don't have the time to spare cycling between wounded lieutenants.

Try to minimize not just deaths, but shots fired at you. In XCOM 2, the best offense is a good defense. Your first few missions should all be Flawless, no wounds; ideally not a single shot fired at your units. Use flashbangs liberally; they make up over half my grenade arsenal. Get used to flanking, elevation and high cover.