The type of string really depends on the type of sound you like. The "boomers" mentioned in the other answer is a good brand that doesn't cost too much.
For a brighter sound, you might go with Dean Markley "Blue Steel". They are cryogenically frozen in their process which apparently gives them their unique sound.
I've been trying another brand that has good longevity, called Elites. They cost a bit more, but seem to last twice as long. They are coated with this weird stuff that keeps them from getting gunked up, but it doesn't appear to diminish the quality of the sound. They have a good ability to play bright, boomy, or mellow.
If you are new to playing....OR if you want a very mellow/dull sound, you can use flatwound strings. Sometimes this is good for music where you want the electric bass to sound more like a upright bass.
Boiling your strings will work a couple times (except for the Elites). It will bring a great deal of life back into the strings, but I've noticed that they will dull about half the time after each boil. So if your new strings last 6 months and then you boil, they'll get dull in about 3 months. Boil again and you'll have about 6 weeks. After that it's dimishing returns as the strings will start to show rust spots (more than likely).