I'll do my best to answer all your questions.
Fantasy and
40k are very different games. While they use the same basic stat systems, the similarities quickly fall away between the two. Generally, in Fantasy you have to think in terms of overall synergy and long-term battle planning. I'm not saying you don't do that in
40k, but in Fantasy, there is a much greater emphasis on it.
Likewise, there is far less list-strength emphasis in Fantasy. Again, there are lists that are better and worse than others, but you will not find lists that are used with such frequency to get names in Fantasy; there's no such thing as Draigowing lists in Fantasy. For the most part, a strong tactician can win with a wider variety of lists, and you will rarely get much of an advantage or disadvantage with your basic list construction.
When building an army, you need to consider your units' strength and weaknesses. Force Organization is different than in
40k. In Fantasy, you may spend up to 25% of your points on Lord, 25% on Heroes, -
AT LEAST- 25% on your Core, up to 50% on Special and up to 25% in Rare. Generally, this means finding ways to get a lot out of your core and find their strengths.
As far as 'must-haves' for Fantasy, the only thing I really consider needed is some form of Wizard, but most will tell you a level 4 mage is necessary in 8th edition, I do not believe that as much. It all depends on your playstyle. Also valuable is learning the difference between bus infantry (5 models wide and very deep) and horde infantry (10 models wide). Buses offer durability and a strongpoint for your army to hold off the enemy through ranks and Steadfast while infantry hordes can pump out more damage.
As far as the armies you like, here are my basic thoughts on each:
Warriors of Chaos: The strengths of this army are its basic core troops (Marauders and Chaos warriors are both excellent for different purposes) and the strength of its characters. YOu can have powerful, well-protected wizards and combat characters with very little to fear from anything. Their main weaknesses is that they are elite, so you will have less models, and have almost no shooting.
Deamons: They are different than
40k demons, as you will be deploying normally (no deep strike in fantasy). Their strengths are that they are reliable and will always have some form of ward save (the invul save of Fantasy) so they can take some serious punishment. In addition, each type of daemon can fill their role really well; Bloodletters/crushers are beatsticks of the highest caliber, Tzeentch guys can put out some awesome casting, Nurgle is very durable and so on so on. You also can get some nice variety in your demonic gifts and abilities. Weaknesses for Demons are that they do not have conventional armor, so while they always have a save of some sort...they do not have a GOOD save. They also are a fairly elite army, so losses are always felt.
Vampire Counts are an army that thrives off of magic and battles of attrition. With your magic and cheap, expendable infantry, you can mire your opponents in a mob of zombies or skeletons that they just can't chew through in time for your more powerful units to get to their flanks and start hurting them back. Likewise, your magic is excellent in a support role, allowing you to heal up damaged units. Weaknesses are the relative poor nature of most of their units, outside of the elite
VC units, you will need to choose your fights wisely. Also,
VCs are reliant on keeping your General alive, if you lose him, your army will begin to melt down and crumble. (this was true for the last edition, but I have not read the new
VC book).
Hope that helps!