When shifting a Shimano road triple from the smallest chainring to the middle you need to give the brake lever a big shove. Don't try to ease it into gear. The shifter actually needs to go to the third (out of 4) position to make the chain climb onto the middle ring. If the chain is on the left side of the cassette you may need to trim back to the 2nd position to avoid chainrub.
The barrel adjuster for the front is usually on the downtube where the cable housing stops. Turning the adjuster counter-clockwise will increase tension and help the derailleur move more quickly, but if you add too much tension you can have problems with downshifts.