I need to purchase my studio strobe bulbs, but I am not sure if they are halogen, tungsten or fluorescent bulbs.
What is "halogen" lighting/coloring/temperature?
Halogen lamps are a particular type of incandescent lamp. They tend to run a little hotter than most standard incandescents. The standard for studio lamps is usually 3200 K ("P2") but 3000 K and 3400 K ("P1") studio lamps also exist. Standard incandescents run from around 2600 K to around 3000 K (with higher wattage lamps typically being higher CT than lower wattage lamps), though some are designed to run at 3200 K and even 3400 K. The standard incandescents designed for 3400 K usually have a very short life, and even the 3200 K ones may have a life of around 60 hours. If you are going to standardise on 3200 K incandescent lamps, halogens are the way to go in the long run. Although halogen lamps are a little more efficient than standard incandescent lamps (the higher the CT, the more efficient they are) they are still more inefficient, and hence produce more heat, than fluorescent lamps.
Fluorescent lamps can have CCTs (in their case they have 'correlated colour temperatures' instead of simply 'colour temperatures') anywhere between about 2700 K (called "soft white" by GE) to over 7000 K, though the latter are usually bad for photography. CFLs go up to about 6500 K (called "daylight" by GE). One of the other things you should look out for is the CRI - the colour rendering index - of a fluorescent lamp. This is a measure of how well the very spiky discharge spectrum has been smoothed out. The maximum possible is 100, and you should be looking for anything over about 85, above 90 is excellent, for portraiture (I'm sure that some people will have used lamps with a CRI of 82 and not complained, however). They put out much less heat than incandescents for the same amount of light.
I assume that you are talking about using these lamps for shooting, not just as modelling lamps. It would be helpful if you clarified that.
Although incandescent lamps have the highest light quality (in terms of their perfect CRI) fluorescents with a high enough CRI are often preferred nowadays because of their lower heat output and, of course, lower electricity consumption. You will need quite a lot of light if you are shooting portraits (why do you want to use continuous light for portraits if you also have strobe?)
As Sparky already said, get lamps that have the same CT or CCT - so pick all the same type of fluorescent with the same CCT, for example, such as
these (link) with a CRI of 93 at 5500 K.
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