Fourstaff's guide to Tiger P (and German tanks in general):
Mindset:
Tiger P, as with most other German tanks, is pretty bad at taking damage in general. Due to their less than stellar (alpha) damage, they generally do quite badly in brawling too (exceptions exist as usual). However, with Tiger P's famed 200mm front armour, it allows this little kitten much more flexibility than most other German tanks. Sure, the side armour are still pretty non existent, there are plenty of places you can penetrate from the front, but for longer ranges the 200mm is much more helpful than a hinderance. It is not as impervious to damage like a hull down'ed T29 though.
First few games:
Coming from the VK3001P (piece of crap if you ask me), you should have the top engine, top radio, and unlocked the 88mm/56 (Short 88) and the 10.5mm/28 (derp gun of Pz IV, avoid like a plague). Choice of either the 70mm or the 88/56 is playstyle dependent: some people prefer the short 88 for its higher alpha while others prefer the 70mm's slight penetration increase and accuracy. I personally prefer the short 88's aim-shoot-relocate timing. When playing the short 88 load a few premium shells (3 is more than enough) to for emergency use.
Given the lacklustre damage of those 2 guns (lack or pen/alpha) it is best for you to play as a support, even if you are on top of the list. Follow another slow tank and play accordingly. If you are the top tank, its still important to drive cautiously: every tank can penetrate you from sides and rear given the chance. Don't be afraid to be the front line if you are the top tank though, your 200mm in front is greatly appreciated even if your dps is next to nothing.
Work towards upgrading the suspension: without it you will not be able to mount the long 88 or the new turret. Also consider getting the enhanced torsion bars to mount the long 88 first, but only if you unmount it later using gold. Turret will be your last upgrade since its not a critical part.
With the 88mm L/71:
Congratulations, you have suffered enough (and/or paid the price) to get the long 88, this is when you start to shine in battlefields. Against equal tier and below, the long 88 will perform admirably, allowing you to dish untold amounts of pain. As much as possible, play in areas where you will be having a sniping match, eg. bridge in Mountain Pass. That way you can utilise your superior accuracy and penetration to its best. DPS is still fairly average at best, but the aim-shoot-scoot cycle is quite decent, allowing you to use quite a lot of your theoretical DPS.
Other things:
Standard consumables (extinguisher, small first aid, small repair kit) is almost necessary for this tank: very often a shot will injure someone, getting tracked is fatal and the ocassional fire should be put out immediately. Prioritise your gunner and loader along with guns and tracks, gunner over loader and guns if your tracks are still in working condition.
As for equipment, rammer is pretty standard, the others are open to playstyle. Camo net is useful with camo crew, Binoculars/coated optics are self explanatory. I would load rammer, wet ammo rack and camo but there is no best way of doing this.
Skills and perks: pretty standard, get BIA if mounting improved ventilation, camo for camo net etc. Otherwise consider getting safe stowage (getting ammo racked is never fun), clutch braking for better wiggling along with snap shot.
When you are at the top of the list:
You have the ability (but not necessarily skill and team) to take on the entire opponent team and come out the victor. As always, be careful of arties, you are the prime target of any halfway decent arty player: a moving pinata waiting to be killed. In absence of any arty feel free to be more aggressive. Always consider driving into the thick of battle (eg city of Ruinberg), where you can effectively utilise your high penetrating gun and relatively hard to penetrate front armour. If there other top tanks like IS or T29 decides to go into the city, consider going to the second front and push all the way into your opponent's base.
When you are at the bottom of the list:
Drive safely, and remember to fasten your seatbelts: the long 88 doesn't have enough penetration against most frontal armour of tier 8's, and your speed and traverse rate will make you pretty useless when faced against fast circling vehicles (notably T71 and the French gokarts). That said, be patient and hunt down enemies scouts and mediums. Proceed to the frontline as enemy numbers thin.
Things to avoid:
Anything named Object xxx, arties, ISU 152 , hull down'ed T29, most IS (except IS/IS2) and arties. Also worth avoiding are fast lights, but if you are going with your teammates (as you should) it becomes trivial to handle.
Where to go after Tiger P?
I have not played VK4502A yet, so I cannot comment on that. Tiger plays pretty similarly to Tiger P, with slightly better (but not that noticeable) mobility and should not see the front lines at all unless there are not much enemies left. Ferdinand is always a good choice, playstyle is not entirely dissimilar.
Happy Tanking!
maybe try the french or russian arty line..... you might notice a difference! 
