I'll narrow down your list by talking about all the stars you shouldn't use. You'll find it gives you a pretty narrow range.
Let's start with the exciting ones: neutron stars. These are, technically, stellar remnants, leftovers of massive stars that blew themselves apart in supernovae. Supernovae are, in general, not a good thing for planets - or, in fact, anything that happens to be near the star. Given that planets would form early in a star's life (and hence pre-supernova), in many cases it's unlikely that a planet would survive. Just to mess with us, though (!), there are many cases in which planets somehow survived a supernova. Where the central neutron star is a pulsar, these planets are known as pulsar planets. So, actually, it is possible for planets to exist around neutron stars. If the neutron star is a pulsar, the planet may be bathed in enough radiation that life could not exist, but perhaps life would have a chance if the neutron star is not a pulsar.
Next up: A White dwarf. White dwarfs (or dwarves, depending on your personal preference) are also stellar remnants. They are the remains of stars like our Sun, who have cast off their outer layers as a planetary nebula and are now merely the small remnants of their former cores. Planets can exist around white dwarfs - in fact, it is thought that Mars and all the planets beyond it will continue orbiting the Sun for a period of time after it becomes a white dwarf (Earth, Venus and Mercury will likely be swallowed up). Life on Europa could be given a chance when the star expands into its red giant phase, before it becomes a white dwarf. As a white dwarf, there won't be a lot of light to help shine on Europa - in, fact the Sun will cool into a black dwarf - but Europa could temporarily harbor life.
Now I'll go to supergiants. These are the biggest of them all, the class O and B stars. They live short but exciting lives, often only ten million years or so (to put that in perspective, our Sun has been on the main sequence for about 4.5 billion years, and will live for a few billion more). They are extremely massive and very hot. Planets may or may not form here - it can be hard to detect them. At any rate, complex life will certainly not form on planets around supergiants, because of their short lifespan. Ten million years go by, and fft! You get a supernova.
Next on the table are stars more like the Sun - think G, F, or K stars (A stars are more massive, and giant-like throughout their lives). These are the stars that get people excited, because many are solar analogs - stars like our Sun. They have great potential for harboring life, and many think a star like this should be our first target for an interstellar voyage.
Another cool (pun intended) type of star are red dwarfs. These are low-mass stars. They are cool, small, and long-lived, with potential lifespans of trillions of years. They could have exoplanets - in fact, many that we have discovered do - and could thus support life, if the exoplanet is within the star's habitable zone. Proxima Centauri, the nearest star to our solar system, is a red dwarf.
So out of all the basic types of stars, I'd go with a Sun-like star or a red dwarf. They have the best chances to harbor life, when compared to other types of stars.
As @celtschk pointed out in a comment above, you can change the orbital period of the planet to whatever you like by simply changing how far it is from the star. This is the simplest answer you'll get to that question. To make it more complicated, though, I'll note that if you want life to develop on that planet, you do have some constraints. The planet's orbit must be within the star's habitable zone. For red dwarfs, that means the planet must be reasonably close, and so a year equivalent to 365 Earth days may not be possible in all cases.
I'll clear up the brown dwarf angle here, because there's an important distinction to be made between brown dwarfs and other stars. Brown dwarfs are "failed stars" - they aren't massive enough to sustain hydrogen-1 fusion. They are technically designated as "sub-stellar objects", and have been confused with large planets. Their masses can range anywhere from 13 Jupiter masses to 70-80 Jupiter masses. Because they don't undergo hydrogen-1 fusion, they don't emit a lot of light, and so would be poor choices to harbor life, unless a brown dwarf was orbiting another star.