Should I be able to escape unscathed?
I have no experience with previous XCOM games but am playing on veteran as I enjoy a challenge. Is it feasible or normal to take damage to more than 50% of squad or be losing squad members every mission early on? This does not seem sustainable. My concern would be running out of supplies and always churning through rookies before getting squad members promoted deep into the game.
Solution 1:
Squadmembers getting injured is part of the game. In fact, it is often hard to avoid. You will often encounter situations in which you simply can't do much to avoid taking a hit or two. It's not a problem as long as you have enough soldiers to rotate so you can always field a full team.
Also losing a low-level soldier is not that much of a setback. A new soldier is just 25§. The black-market value of your loot alone is often worth the recruitment price of a few new rookies.
But what can really hurt is losing a high-level soldier. As you progress in the game, the game-balance assumes that your team is leveled appropriately. Most late-game enemies have defense bonuses which counter the aim advantage of high-level soldiers so your hit percentage keeps about the same throughout the game. Also, technology alone won't be enough to counter many of the nasty tricks some late-game enemies have up their sleeves. You will need the overpowered abilities only high-level soldiers have.
This means that later in the game it will become practically impossible to keep building up new rookies (the rebel HQ sometimes allows you to hire some high-level soldiers, though... for a price). Losing a captain or higher in the mid-game can be a drastic setback, and losing multiple of your best soldiers at once often leaves you no option than to load an older savegame.
Solution 2:
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.