If you're after a sports bike then I'd go for a 250cc four stroke engine from Honda, Kawasaki Yamaha or Suzuki, take your pick. I definitely wouldn't bother with anything as low as 125cc as you'll outgrow it fast.
If considering something other than a sports bike then you may want something a bit bigger maybe in the 400-650 range, it really depends on the bike. I have also heard that the Suzuki SV650 is a good bike for beginners. If you are really just riding around town I used to own a Honda vtr250 which was awesome for that purpose, and would be a really easy bike to learn on, but it wouldn't really be suitable for long trips on the highway or anything like that.
Finally, I'm not sure of your budget but buying second hand is never really a bad idea for a first bike, as its less worry if you drop it, and you'll lose less money on the sale when you decide to upgrade. Use the money saved for decent helmet and other riding gear. (Well, you should be getting that anyway!)
If considering something other than a sports bike then you may want something a bit bigger maybe in the 400-650 range, it really depends on the bike. I have also heard that the Suzuki SV650 is a good bike for beginners. If you are really just riding around town I used to own a Honda vtr250 which was awesome for that purpose, and would be a really easy bike to learn on, but it wouldn't really be suitable for long trips on the highway or anything like that.
Finally, I'm not sure of your budget but buying second hand is never really a bad idea for a first bike, as its less worry if you drop it, and you'll lose less money on the sale when you decide to upgrade. Use the money saved for decent helmet and other riding gear. (Well, you should be getting that anyway!)