Medication does help. If you're wary, I would recommend trying therapy for a while and deciding if you think that's enough. Either is better than just not doing anything.
As has been said, doctors will almost always go for an SSRI of some kind initially, and at the lowest available dose. Which one probably depends most on what their prior patients have had success with before. There are no hard rules, and they're all similar enough to be somewhat interchangeable. While some may be advertised for specific conditions, that's mostly because they've been specifically studied for it, not because it's particularly more effective than other SSRIs.
Some SSRIs seem to be worse than others in terms of side effects (fluoxetine (Prozac) appears to be less trouble than paroxetine (Paxil), for instance), and some side effects may only appear at higher dosages.
One thing many people don't know is that with some medications and SSRIs in particular is that they take a month or so to really take effect. You can't simply take one and decide whether it works or not. Unfortunately, the worst of the side effects happen in that first month before going away, which which makes many give up on them. (Don't do this!) The long list of side effects you may read about is a list of things that you may experience at some point, not things that are constant.
Discontinuing medication worries a lot of people too. In my experience, coming off of an SSRI without tapering is only about as bad as the initial side effects, and lasts a few weeks. Mostly characterized by some dizzy sensations and "zaps" or "shocks" in your temples. It's annoying, but I don't think it'd be worth avoiding medication entirely over it.
If you have panic attacks a doctor may add benzodiazepines (Valium, Klonopin, Ativan, Xanax). Usually only ten or so at a time, for taking as you need them, not daily. The effect is a pretty significant reduction in your anxiety for a few hours at a time, just enough to get through a particularly tough experience. A doctor may be reluctant (and rightfully so) to hand these out on first meeting, though, as they can be abused.
Sometimes people get on a certain dosage daily, but I would be very wary of this as it's said to be very hard to come off of. It also won't do anything for depression.
So that's what to expect; an SSRI or an SSRI+benzo. Whether this is "best" is still an open question, but it's the most common and probably best-studied course. You'll still want to talk to the prescribing doctor every few months about whether you think it's really working for you, and try other things if not.
I personally found bupropion (Wellbutrin) to work well, and quickly, but I was only able to get a month's worth from a friend when I was in very bad shape. I intend to suggest it specifically the next time I can afford to see a doctor, even though it isn't (yet) widely used for social anxiety. (NB: This is just an anecdote in a sea of anecdotes. I'd still recommend trying an SSRI first.)