What are the appropriate times to use AP and HE shells respectively? I've been using AP against most targets, switching to HE only for thin-skinned vehicles to avoid straight-through shots. Maybe I'm too influenced by more realistic tank sims.
I've started on german tank destroyers now and been having great success. Best so far is a 5-kill battle with the panzerjäger, currently using the Marder II with the first 75mm gun (great for the sound effect alone) and getting kills in almost all battles. I've also researched the A-20 tank.
You have it about right, HE should be used on lightly skinned targets like SPGs and scouts as well as targets you have no hope of penetrating like a tier 10 heavy. HE is handy because it almost always inflicts damage, even if only a fraction of its potential, on a target. HE is also handy for inflicting module damage on the Hun, though module damage is not assured and may be more easily achieved by AP'ing enemy weak spots. Example: nail a T-44 with HE on the rear, and rear sides of his turret with a decent caliber of HE round and you may be rewarded with watching his ammo rack blow, and his tank may be reduced to smithereens.
Of the vehicles I've played and unlocked, I generally play a tier or two lower. I've kept the following: a StugIII, an SU85, a PanzerIII, a VK3002DB, a Tiger, and a Panther. I'm also training up an American medium while I wait for the Yank TD tree. I stick to the vehicles that easily make cash without premium, for me, and I'm enjoying running a battle or two per day. Some of the higher tier vehicles are quite enjoyable, like the JagdPanther, but I enjoy mid-tier play more than the top or bottom tiers as I am vulnerable to any vehicle and yet still able to hurt anything else on the battlefield.
The German TD tree will teach you how to play a TD, well. After playing the German tree you'll then be able to move over to the Soviet tree with ease after grinding the likes of the Hetzer. The PzJager is a fun little sniper, as is the Marder II. Ambush and snipe, keep to that 'cause if you haven't assimilated those lessons by the time you reach the Hetzer you are going to want to quit the German TD line. The Hetzer will instill many hard lessons, but you'll be a much better player for it. The lack of mobility present in the Hetzer will force you to choose your ambush locations with a greater attention to foresight, if you want to survive. My personal opinion is to avoid the 105mm on the Hetzer as it will force you into shorter range engagements where you will be spotted and flanked by enemy tanks, or more likely you will have an arty round dropped on you because you are engaging within spotting distance. I played the Hetzer, and enjoyed it, by using it as a hard to spot sniper. Once you learn to anticipate the flow of battle you'll be able to move your Hetzer about in response to situations that have yet to develop or escalate, and so once you move on to the Stug or the JgPanzerIV you'll be deadly at range and with enough mobility to keep your front-line allies covered. The 105mm can be handy if you're just looking to 'skip' the Hetzer, but if that's the case you'd be better off to use free experience to run through the research tree as you really should be switching the long 75mm once you get into the Stug, rather than playing a mid range sniper/brawler.
If you find the short 105mm on the Hetzer to be more your style, then drop the German TD line and go with the Soviet TD tree. The Germans are about accurate long range fire, the Soviets are about raw firepower at mid-range. The Soviet TD tree also doesn't have a speed bump like the Hetzer to slow your enjoyment of the game. The SU85b, unlike the Hetzer, is a super easy grind as the 85mm is a fantastic HE chucker and will earn lots of XP from shooting at anything and everything, quickly at that. The SU85 proper is a slightly less mobile Stug, until you get the 107mm gun on it, and then it becomes a murderous fiend. My SU85 will two shot a VK3xx1, from the front, at mid range before I am spotted. Anything tier 5 or lower is often a KO at the first shot. My Stug can open fire and reliably hit the same targets from a longer range, but will require three to five times as many rounds to put a similar target down. The Stug will snipe the SU85 from long range in 3 to five shots, depending on bounces. The SU85 will KO the Stug from slightly above mid-range with one shot. The SU85 will also bounce the very occasional enemy round due to sloped armour. The Stug will not. Both are fun vehicles, but are also dependent on two different styles of play.