1. Age magic - immortality.
This one is easy in the sense that you don't need to come up with as many rules. You also have a simplistic magic element that can HUGELY affects the world you create. How do people feel about the immortals. What do the immortals do with their immortality? Where did it come from and can it be shared. Etc.
2. General magic - fireballs and healing
This is kind of the Merlin magic, where everything and anything can be done if you know how. It's been renamed in many books with different rules, but the main thing about it is that it isn't a specific isolated ability.
3. Superhero - single power or sets.
Here you have the isolated ability or abilities. Invisibility, absorption, can throw fireballs (but nothing else). Usually it comes from a reaction to a foreign element or some kind of inborn ability. You can go a lot of ways with this and how the people with these abilities (born or learned) are regulated in the world.
4. Race magic - racial quality.
This ties in with super hero magic. Mind reading, ESP, nightvision, and so on. Here it is attached to a race instead of a single person. With this you have to make a world where these abilities can exist without their causing a devolution. If humans gained mind reading as a race, we'd probably all be in a lot of trouble.
5. Science - alchemy, symbioses, futuristic.
Science fiction, but not science fiction. What I mean by this is scientifically based magic, but where the characters do not know or understand science, and so to them it is magic. For instance, something like the Venom suit from Spider Man isn't really magic, but to a normal person on earth, it sure looks like a monster from hell.
What I do when I have a magic idea is then run it through some tests. What do I want my character to do with it. If he does this, what will happen. I work as hard as I can to invalidate my idea, then try to fix the problems, until I end up with a system that works.
Another thing you can do, which is the opposite of what another poster said, is to write the story first, or at least the outline. Then go through it and in places where things happen, [Hero wins contest] you can think about how magic might have been involved here, rather than him just being physically stronger. Or if there is a battle, and the enemy escapes, come up with magical reasons instead of luck and a fast horse. It's kind of like reading a history book, which tells you "this happened and this happened and this happened" but doesn't always tell you how. I think it could help you with coming up with ideas when you have specific circumstances for the magic to be used.
Anyway, hope that was helpful.