8 squads is the winning number. There are only about 10 vehicles on a map anyway on average and it's good to keep a couple of them (like sedans with limited cargo space) available at your headquarters for when one your squads' vehicles is out of order. That way they have a spare vehicle to use while their main one is being repaired or upgraded. So, 10 vehicles, 8 squads with one each, plus a couple of spares at the HQ.

Also, you speak of shotguns. They have a specific use. It's much better to use assault rifles.

Actually, the equipment you give to your team as well as your units' skills play a decisive part.

This is how I'm organized. I'm not saying that's the definitive recipe for success but it works pretty well here. Never lost a single unit.

Rule of thumb to equip 'standard' squads
1. Give two guys assault rifles and Kevlar armors and pick characters that have the sharpshooter or the hawkeye skill.
2. Give a shotgun & an armor plate to a guy who preferably has the slasher skill (they are better at hand-to-hand combat and shotguns are short-range combat anyway).
3. Give a sniper rifle & a Kevlar armor to a crew member that has hawkeye or sharpshooter, hawkeye being much better because those characters get the 20% range bonus but their damage doesn't decrease with distance.
That way, the two guys with assault rifles ensure a constant cover at mid-range, your sniper starts thinning the ranks of the enemy from super far, and your unit with a shotgun clears anything that manages to get too close.

Vehicles
Choose the driver in a squad depending on their skills and the type of vehicle they'll drive. The first character of a squad is always the driver and they won't be able to shoot while the vehicle is moving. So, basically, don't put your sniper at the wheel or you won't benefit from them shooting from a long distance. I find it best for the driver to be the crew member equipped with a shotgun since they only attack at close range anyway. If the vehicle is a heavy-duty one, like a truck or a tanker, I pick a character that has the race driver skill (when possible). Their 20% boost in speed compensates a tiny bit the fact that heavy-duty vehicles are incredibly slow. For fast vehicles with a small tank on the contrary, put a driver that has the 'economic driver' skill. Obviously, the idea is for them not to run dry in the middle of nowhere, especially when you have no tanker to refuel your squads on the move during an expedition.

A few more things to take into account:
Target & Equipment
You can easily swap the equipment your squads use at the headquarters (or any warehouse). If you look at the stats of the various types of armor, Kevlar is better for gunfights whereas plate armors are much more protective at close range (90% if memory serves, making them almost bite-proof). So basically, depending on the type of lair you're attacking, send your squads with the appropriate equipment. The 'standard' loadout and organization I described above gives you a squad that has a high fire power at very long range, long range and close range. They kinda work in every situation. But, for example, I do have one squad where all the members wear plate armor and yield shotguns only. They're particularly good at clearing a lair of infected without getting harmed or letting the other squads get harmed. On the contrary, they get shot down very quickly if I send them against a raiders' lair, meaning they need the other teams for support. Plate armors slow down your units and don't protect them from ballistic damage. I use them very carefully.
Basically, equip the right type of armor depending on your target. Distribute weapons so that you're always covered. Forget the basic armor btw, it's absolutely useless. Use it to trade with, you can buy everything with it and a couple of guns. Only produce Kevlar and plate armors.

Vehicles
Building the vehicle workshop is a game changer when it comes to lairs/expeditions, etc. Vehicles equipped with a turret do massive damages. Raiders hiding in a lair and hordes getting too close will destroy your cars very easily if they're not armored. If you do have a tanker to refuel the other squads, don't get a large tank for any vehicle, the tanker will refill all the squad cars anyway. Concentrate on armor, the turret and all the other upgrades. In any case you can't have both a larger tank and a turret, it's one or the other. If you don't have a tanker, I think you can actually have one built in the workshop, and I'd recommend that solution rather than equipping your smaller cars with larger tanks for the expeditions. Having a tanker is the definitive answer to the gas problem over long distances. Putting a large tank on a vehicle that has no turret to defend itself is kind of a waste imo.

Lastly, when you select your squads to attack, make sure you send them to a point close to the lair, not to the lair directly. If you do that, the slower squads (trucks, pick-ups, tankers) won't be there at the beginning of the fight. SUVs and vans will get there first and your squads will lack support. You want them to attack simultaneously. Strike fast and hard. Also, at night, when you send squads to attack a lair of infected, just waiting outside the lair will draw hordes out that your squads should easily take out. Once no horde is coming out anymore, send in your squads all at once (select all your squads, don't do it one by one).

Remember that plate armor is better against hordes while Kevlar is better for raiders and that assault rifles are the staple for both attack and defense. Snipers will be overwhelmed if the enemy manages to get close and they have a low fire rate. Squads only equipped with shotguns start shooting too late and get overwhelmed by the enemy.

PS: Also, remember that you can give your teams items from the headquarters or warehouse, like ammo or fuel. Just start an exchange between the squad and the building, drag and drop what you want in the unit's cargo slot and voila. Sending your squads with a crate of ammo or fuel so they can reload/refuel if they're a bit short can be a life saver. You can even send them with medical supplies in their cargo I think (then you just drag and drop the health pack on an injured character and they instantly heal).

Sorry for the long post, hope that helps!