Pick a starting location

The Throne Room
This is by far the most commonly presented starting location, and makes it fairly easy to complete the game.

A Spider Room
This is perhaps the best starting point, placing you very near the shield, which is a good first object to collect.

The Witch's Bedroom
If you're unlucky enough to start here, quickly get out; without the protection of the crown, the flying magic will kill you, and you can't cut the witch's hair without the scissors.

The Cup Room
Although this allows you to grab the cup straight away, you can't escape from this room without losing a life.

The Scissors Room
Starting at the bottom of the castle is a nuisance, since you'll have to go most of the way up and then halfway down again to successfully complete the game.

A Gargoyle Room
A Dining Room
A Magic Room
These are all fairly bad places to start, since you have little choice but to go and get the scissors (and perhaps the axe) before doing the whole trek right up the castle and back again. The only compensation is that you can instantly load up on magic in two of them, and they only pop up as starting locations fairly rarely.