Would you like to swing 'round a star?

Continuing along earlier lines of constructing your very own habitable planet for science-fictional purposes, it's useful to consider what type of star you want to build your "solar system" around. (More accurately, "stellar system", since solar refers to our own sun.)

For the purposes of this discussion we'll stick to "adult" stars - stars that are on what astronomers call the main sequence. Older stars which leave the main sequence may puff up into "giant" or "supergiant" stars for a while, but these stages tend to last for only a tenth or so of the star's lifetime - the remaining nine-tenths are on the main sequence. So we'll set aside, for example, red giant stars for another discussion.

Follow up:

When talking about main-sequence stars (only), there are are a number of properties of any given star, and most of the major ones relate back to the star's mass. Thus:

• The more massive a star, the more luminous it is. (A star's luminosity is the amount of energy it radiates per second.) This relationship is quite steep - a star with ten times the mass of our Sun would have more than three thousand times our Sun's luminosity. So your planet would have to be far out from a high-mass star to avoid being bathed rather a lot of radiation from that star.
• The more massive a star, the shorter its lifetime. Live fast, die young: the high-mass stars are giving off energy at a tremendous rate (see above) and thus are headed toward an early burnout. Our Sun's lifetime will run about 10 billion years and change; for a star fifty times our Sun's mass, we're talking a lifetime of a few million years at best. Better not pick the highest-mass stars for your fictional system - by the time life had evolved to the point of multi-celled critters, the star would have blown itself up, putting a short and nasty end to all that.
• The more massive a star, the hotter its surface temperature. Now, an object's color depends on its temperature - think of heating up a piece of metal. You can get it to red-hot, then white-hot (which is actually a combination of "middle" colors), and if you could get it hotter still without melting it, it would go all the way to blue-hot. So hotter stars are more blue, cooler stars are more red. The massive, luminous, short-lived types are hot blue stars - which, as I suggested above, might not be the best places to put planets around. Obviously, a pleasant yellow star like ours works out well, but you might also make do with a cool red star, as long as you put your planet in close enough to be reasonably warmed by that star.
• Finally, more massive a star, the greater its size. As I said, this doesn't count the giants and supergiants that stars can become in their later ages - we're still just talking about the main-sequence types. So those aforementioned cool red stars are also pretty dinky compared to the more massive blue types. (One can call these little guys "red dwarfs", but you run into some tricky nomenclature there - technically all main sequence stars are "dwarfs", to distinguish them from the later "giant" stages. But if you ever wondered about what a "red dwarf" is, now you know.)

So to sum up: you want a star without too much radiation, and with a lifetime of at least a few billion years. That limits you to stars of a few times the mass of our Sun or below. (Such stars would appear white, yellow, orange, or red as you go to lower masses - and temperatures.) The less massive (and smaller) they are, the cooler (and redder) they are, and the less luminous they are; so you'll need to put your planet closer in to get the star's full benefits.