So, you wish to use standard armour piercing weapons, high explosives and incendiary weapons, eh?
Hmm, let's see...
For Armour piercing weapons, being one of the weaker weapons in this game (I say weaker because the damage levels are really low for almost all the weapons), the one thing you really must familiarise yourself with is your enemy's armour levels. Okay, so you needn't memorise it, but you should have a general idea of what you're up against.
Basically, sectoids, floaters and snakemen all fall into the category of having very light armour. Practically all terrorists, mutons and ethereals have relatively medium to very heavy armour. For all the aliens, the front armour is the hardest, followed by the sides, the rear and finally the under-armour. Only explosives affect under-armour. So for the best effects, try to shoot them from the side or in the back if you're having trouble.
Your two basic armour piercing weapons are the standard pistol and the standard rifle. The standard pistol is just as accurate as the rifle for snapshots, but it is very fast firing. You make up for its lack strength and lack of aimed accuracy and autofire by its sheer speed and cheapness (sure, it's just 1 extra snapshot over the rifle, but better an extra shot at the higher snap-shot accuracy, right?). The rifle has an autofire option, which makes it decent for short range combat, and a slow but accurate aimed shot, making it a slow but fair sniping weapon. The difference between their damage levels is only 4 points, so they're technically interchangeable. Note however, that of all the aliens, the only real aliens they'll be able to deal with are the sectoids, snakemen and floaters (at least on superhuman - on easier levels, you can take out cyberdiscs and reapers too).
Your next set of armour piercing weapons are the heavy cannon, auto-cannon and tank cannon. The heavy cannon features strength and accuracy, while the auto-cannon features an auto-fire mode albeit it is not as strong as your heavy cannon. While you'll normally want to use these with HE shells, the AP shells are useful for taking out certain enemies in the early game who are resistant to HE. Such as chryssalids (who take less damage from explosives but take normal damage from AP shells). The tank cannon is the strongest AP weapon in the game, sadly, it's stuck on a tank with its poor accuracy and bulk. However, it is still powerful, and can take out cyberdiscs a lot easier than the rocket tank.
Apart from knowing who to use the AP shells against, you'd mostly use them in the same manner as you would your energy weapons.
Note: For pistols and rifles, as mentioned before, they are best used for attacking sectoids, snakemen and floaters. You don't want to end up facing a bunch of enemies that you cannot defeat. They are best used in combination with explosive weapons - namely grenades. Cannons with HE shells work okay, but they lack strength for taking out some of the stronger terrorists. For these, you'd need large rockets and high explosives. For most other enemies, alien grenades and proximity mines work wonders.
Also note that the pistols, next to the laser pistols, are the best weapons in the game to use as reaction-fire weapons. Or, if you prefer, reaction fire 'training' weapons.
Well, there are plenty of strategies you can use with grenades. Like pre-arming the grenades and storing them in your shoulder slots or belt for quick retrieval. The grenade relay chain, where someone at the back arms a grenade and tosses it forward to where it's needed so that the scout can toss it and also run away or fire off shots.
You must throw the grenade in order to earn any experience from it. Dropping it, while effective, will not net you any experience.
Strength is the major influencing stat used by grenades, as it affects the distance of the throw. Throwing skill just controls where it lands. High explosives are literally twice as heavy as any other grenade, so the throwing distance is halved. Hence why you need plenty of strength to make use of them effectively. But they pack a punch!
If you're standing under a ceiling of some sort (well, the Skyranger's wings are technically a ceiling), your throwing distance can be drastically altered. Walk away so that you're no longer under the ceiling before attempting your throw. Otherwise you'll only be able to throw short distances. This is why it's so difficult for strong soldiers to throw grenades in cramped spaces, like the bases.
And just so you know, hitting enemies with grenades exercises the firing accuracy stat. So soldier that cannot shoot well but have overall good stats might want to be kept around as grenadiers for a while.
Ranged HE weapons
Well, there's the autocannon and heavy cannon. One with speed and the other with power and slightly more accuracy. As a lot of enemies have light under-armour, HE shells are the natural choice for these weapons. Note that if you're wearing power armour, these weapons become even more lethal because you can now use them as short range combat weapons. You'll only receive damage from direct hits, not the splash damage. Or little to no damage in the case of heavy cannons, being slightly stronger.
The rocket launcher is your second most powerful handheld ranged HE weapon (the Blaster launcher's the first). It's the most accurate aimed shot weapon in the game as well, so always try to use these with aimed shots and with kneeling and very accurate soldiers. Snap shots should be used when you're sure of a hit. Like firing from a high elevation right into the ground near a group of enemy, or firing it right into a wall.
Small rockets are not that powerful, but they are much more portable than the other rockets. They're about as powerful as a standard grenade. Still good for training. Also, in power armour, you can almost use these as close combat weapons. Not as effective as an autocannon though.
Large rockets are the
rockets to use. You'll need some way of distributing the weight if you find them too heavy. Save these for clusters of enemies, or for tough enemies. Great against Mutons and Ethereals and practically everything else. Sectopods may need multiple hits, but will go down to large rocket eventually.
In general, lots of people use incendiary weapons as a very temporary but portable (and expensive) light source. Fire can be used to indirectly kill enemies over several turns(as long as the fire keeps burning and there's fuel to burn).
Incendiary weapons also have one very unusual effect. Any unit that is standing in a patch of fire will receive impact damage for every incendiary shell/rocket that detonates during that turn. Amazing, but true. Note, this may only be true for fire created in the current game. Not too sure about what happens if you save then reload. This is technically a cheat.
Unusually enough, you can even kill superhuman sectopods with autocannon incendiary rounds this way.
The incendiary rocket is the heaviest of the rockets. It also has the highest impact damage and blast/burn radius of any incendiary weapon in the game. I'd recommend using it as an opening move or if you want to deal tons of damage to units who are standing on fire. Note that there's a limit to how many fires that can be created at any given time, so using a lot of these is not recommended unless it's for the impact damage.
Overall, any of these weapons can last all the way through the game. Even pistols. You just need to know how to get the most out of your chosen weapon and when not to use them. Anyone can use a laser rifle or a heavy plasma, but with the other weapons, you need to use combinations to make up for their weaknesses.
But look, don't force yourself to use these weapons if they don't seem to be working for you.
Curses, I timed out while typing all this ... And somehow I get the feeling I'm not answering the question. oh well
NKF, narrow minded fuddy duddy who refuses to let go of the past and will not accept anything newer than 1979.