It's all so super individual. A friend of mine got super hyper on one med that really helped me relax. I also started a sleeping pill that kept me wide awake! But it helped my mood, so I take it at noon. Go figure. So, I don't feel like answering what kind of side effects I've had will be helpful. For whatever you end up on, just look over the list of potential side effects so you are personally aware.
Do you know if you'll be looking at something like an SSRI (like Paxil, or something you take daily), or something more for immediate and acute anxiety, like a benzodiazepine (Xanax, etc)? Benzos are no problem for me...even the one I took that was supposed to knock me out and help me sleep just made me a little relaxed. Super mild. For me, that's not necessarily good at all...my tolerance can increase too fast and I have a bad addiction history (not to benzos, but that could easily be next if I don't watch out).
If you've never taken meds for anxiety, hopefully your doctor has a good understanding of what your anxiety is like and can at least give you a starting point. I'll only say that if one med doesn't work, there are several other options within the same class and also very unrelated classes. For example, SSRIs do not work well for me (but work well for others), but alternatives like gabapentin (anti-convulsant) makes me more generally relaxed. Benzos would be great but I can't have a regular prescription and need to dump the sleeping pill benzo very soon before I make my sleep problems worse through dependence (if you have regular night terrors, I'd avoid a benzo sleep med...I alternate my sleeping medications so I don't get dependent on any one too badly...my sleeping problems are quite chronic).