This question gets a bit tricky to answer... Starting from scratch, if you buy just vanilla WoW, you can experience the original world as it has been destroyed by the Cataclysm expansion. You can level up to level 60, but cannot access professions, areas, races, or other such things from any of the other expansions.
In order to access Outland, jewelcrafting profession, and Draenei? / Blood Elf races and starting areas, and level 61-70, you will need vanilla WoW + the Burning Crusade expansion.
In order to access Northrend, Inscription profession, and Death Knight class, and level 71-80, you will need vanilla Wow, Burning Crusade expansion, and Wrath of the Lich King expansion. Oh, and a prior level 55+ character on your account to play as a Death Knight.
In order to access the misc Cataclysm level 80+ areas, Archeology secondary profession, Worgen / Goblin races, and level 81-85, you will need vanilla WoW, Burning Crusade expanion, Wrath of the Lich King expansion, and the Cataclysm expansion.
Those are the restrictions. You can play on whatever realm you want with whoever you wish. You just may not be able to reach all the areas they can.
You can trial every bit of it with the 10 day trial, though I don't quite know how they treat it when your time is up.
The Lich King can actually be found in many different places, including the Death Knight starter zone, several 5-man dungeons and appears as a result of many quests in Icecrown Citadel. If you level normally throughout the "Wrath of the Lich King" expansion, you will encounter him on several occasions.
To actually battle him, you need up to 25 other players in the Icecrown Citadel raid instance. For him to properly spawn, all three wing Guardians (Sindragosa, Blood-Queen Lana'thel and Professor Putricide) must be downed. Doing so allows you to teleport to him through the center of the Citadel. I believe even if you somehow got up to the top of the Citadel, he will not spawn unless those preconditions are met.
Best Answer
There's a few ways to do this. If you just want to quickly check snapshot of prices without regard for the economy of your particular server, just check Wowhead.
Wowhead displays the items vendor value, as well as the average auction buyout price across all servers.
However, this information is sub-par in that not every servers economy is the same, and in fact substantial price swings occur across realms. Also, for items that are less frequently traded, there may be little to no data.
If you want a more detailed picture, you need to go to the source from which WoWhead derives it's average; The Undermine Journal by contrast, provides a much more comprehensive picture, giving you price history and current pricing data for any item, specific to your realm and faction, as well as the cost of component materials for crafted items, should you wish to just produce them yourself or ask a friend to. Additionally, TUJ distributes an add-on that will allow you to view historic data for an item in game while browsing the AH.
As you can see from this screenshot, The Undermine Journal is far more detailed, as well as providing a more specific and accurate picture - for instance, the item in question (Flask of the Winds again), is roughly 30% more expensive at the Ysera-Alliance auction house than Wowheads average across realms indicated.
(European players will note that TUJ EU site is found here.)