I'm researching my new road bike too. Here's info on shimano road sets, originally from: http://www.chainreactionhub.com/road/980-our-guide-to-shimanos-road-groupsets-from-tiagra-to-dura-ace
with some additional comments by me.
Common: All of these have shifter mechanisms in the brakes, so they're "brifters" Nothing road-based has thumb shifters like a MTB.
1) Claris, 8 speed and lowest spec. Probably not under active development any more. However it'll still work better than most old bikes because its indexed. Plus its cheap, having earned back its R&D costs.
6/7/8 speed all use the same chain sizes.
2) Sora, 9 speed. Relatively uncommon on new bikes becuase 10 is a two-digit number (that's the reverse of Shopkeeper's pricing theorum where another digit makes it look more than just one more.)
3) Tiagra, 10 speed, but better at shifting than claris and sora
4) 105, 11 speed now, lighter and stiffer and cleaner action than tiagra
5) Ultegra, 11 speed, as much better than 105 as 105 is above tiagra
6) Dura-ace, 11 speed, basically the top spec mechanisms as used by pros. Expect to sell your house to buy this level.
Ultegra and Dura-ace can also be had with Di2, which is electronic shifting. This means a little battery and motor haul the derailer rather than you pulling a wire. The gear change still happens because of your chain motion, same as normal.
You should consider the offerings by sram too.
Older versions of the same group set may have fewer gears... 105 used to be a 10 speed, and really old ultegra was a 6 speed in the beginning, and gears increase over time.
There is a trickle-down effect that comes from technical advances in the modern groupsets too - that's probably why Ultegra has an option for electronic shifting, originally designed for dura-ace. That's probably a bad example given its such an expensive change, but something like a ramp and pin design for smoother shifting would trickle down to the 105 then to the tiagra, by which time sora and claris will have vanished.
Personally I'm aiming for 105 level, (if I can get it in my price range) with aluminium frame and disk brakes.
Note also that you don't have to get the full groupset - brakes and transmission are only in common at the brifter, so you can use anything with the same cable pull distances.