How can I adjust index shifter so it doesn't skip the second chainring? I recently replaced my chain and cassette on my commuter bike.  It was a first time operation for me, as I am a new to doing bike maintenance.  That part seems to have gone fine.  While I was at it, I decided to adjust my front deraileur since it was rubbing a bit in certain gears.  I seem to have messed everything up while I was playing with it.

The guide I was reading said to adjust the lower limit and check that it doesn't rub for the whole range of gears on the rear cassette.  By the time I had concluded that there was no way that was going to happen and I would just have to avoid silly front/rear gear combinations, I'd messed up everything.

When I do a single full up-shift click on the shifter, the deraileur moves far enough to take the chain from the smallest chainring to to the largest chainring, skipping over the middle one.  The little window on the shifter says "2", and it won't go up to "3" since I've maxed out the high stop on the deraileur.  Downshifting drops it all the way back to the small chainring.  If I disconnect the cable from the deraileur with the only tension being me holding the other end of the cable, the shifter works like I'd expect.  It nicely clicks through 1-3 and back again.

It seems to me that I twiddled something that makes the shifter pull more cable with each click than it used to, but I can't figure out what that might have been.  Alternately, I've done something else completely knuckleheaded.  

The bike is a 2008 Raleigh Cadent FT2 with ST R225 shifters.  Except for a spoke and the afore-mentioned chain and cassette, everything is stock.

Can anyone help a newbie figure this out?
You went at it backwards.  First thing to do (after backing off the limit adjustments a bit) is to adjust the barrel adjuster so that you can hit middle gear, then adjust the upper and lower limits so that you hit the outer two without going too far.  Then you can "tweak" the barrel adjuster slightly so that you minimize chain rub at the rear without upsetting clean shifting to the middle gear at the front (then "tweak" the limits again).