Mortain is quite a difficult mission because resources are tight, and if you do not want to recycle a lot of your initial infantry, your unit choices are also very tight. Because we do not sacrifice units unnecessarily and try to keep all units alive, we were basically stuck with the initial units. This may handicap you later in Mission 13 - Mortain Counterattack because you start with the units you finished with, plus initial reinforcements of three tanks, which puts you well over your Population Cap, further limiting your ability to choose units.
In the screenshot below, you can see our final units after defeating the final wave with a bit of time to spare. All objectives completed.
Part 1 - Initial troops and Command Points
You do not have access to heavy tanks, and your HQ / Retreat point is far to the west. You do have a single M2 105 mm Howitzer which gives you artillery bombardment for free, but with an 85 second cooldown time. Use this early except in the second half of the mission when you will want to shell tanks.
The enemy will have increasing amounts of infantry, some light vehicles, and then heavy tanks.
There is a small cache of resources around north of middle of the map, hidden behind some trees.
For units, build one or two halftracks right away and change them into MGMCs. These will be your earliest anti-infantry units and you will run them around as "firefighters" against infantry -- that is, race them to where the enemy approach. Once a couple of waves go by, you should be able to tell where the enemy consistently come from and park them at the ready.
Always have the MGMCs take point to protect your infantry, who should be doing pretty much nothing except building free structures like tank traps (once you get the Infantry Company: Defensive Operations ability) when they are idle, or manning AT guns.
One additional unit of Engineers will probably come in handy, so build them after your first or second halftrack.
Use your first halftrack to relieve the Rangers to the west and add them to your units.
While building the halftracks, grab strategic points and start putting Listening Posts on them, starting with Fuel (to quickly get more vehicles) and then Ammo.
Engineers should start blocking roads with Tank Traps. You don't have a lot of resources yet, so just build free structures to keep collecting Command Points. Aim to quickly get Off-Map Artillery Support to give you a second bombardment ability against enemy tanks.
As resources come in, start adding M8 Greyhounds and fully upgrading them.
Once your Population Cap is full, redirect resources toward building Machine Gun Emplacements. These are priceless against heavy tanks because they act as sturdy decoys to soak damage, allowing you to position AT guns further behind them and generally safe from being shot at because the Machine Gun Emplacement is in front and closer to the enemy. In this way if you know where the enemy vehicles are coming, you can shield your infantry from them with a no-population-cap structure.
Note that even on Expert Difficulty your Greyhounds can typically take a couple of shots to the front before having to retreat, if you desperately need some cover for your infantry (e.g., for your Engineers to build something), to stall a tank for bombardment, or to just stall the enemy advance.
Part 2 - Defending
Initially, spread out your vehicles to intercept and delay/pin infantry as soon as possible and direct vehicles that are not engaged to the incursion location.
Fighting infantry-versus-infantry is a losing game on Expert Difficulty because the enemy just needs to get close to flame your units with their Pioneers, or they start sniping them in the later game. For the same reason, Machine Gun Teams are useless as the first line of defense as you can't pull them back fast enough.
MGMCs and Greyhounds can generally out-last any infantry if they can be kept pinned but enemy infantry start to have Panzerschreks so a single vehicle is dangerous to field later in the mission. They can pin units and thereby protect themselves from being hit by anti-tank weapons, but it's better not to chance it.
To get them to stop, either plant a vehicle in front of them or, in the case of tanks, have something disposable for them to shoot at, such as a Machine Gun Emplacement or a Listening Post. Even an armour-skirted Greyhound can be a temporary shield if necessary. Once they stop to shoot, call in a strike as soon as possible. Mortars are also very useful here. AT guns are vulnerable but if you can put them behind a disposable shield, they also do very well against vehicles.
Infantry should not engage unless they really have to -- even the Rangers, which are really your emergency team against tanks.
Keep building Machine Gun Emplacements to help pin the increasing amounts of enemy infantry.
Reinforce infantry in the field when you can, using your MGMCs.
When you get the chance, mine the roads near the spawn points. If you are worried about infantry getting attacked suddenly, send a Greyhound to do it.
The video below (difficulty unknown) shows an interesting passive Mortain defense where infantry basically huddle on the hill and defend until the timer runs out. I haven't tried it on Expert, but if you find a wide perimeter hard to coordinate, you could try the mission this way.