Bicycle Mechanics - Front derailleur adjustment

Hi, I just purchased a 21 speed mountain bike. It has a Shimano Tourney FD-TZ30 derailleur. I adjusted to back derailleur without any issues but I am haveing problems with the front. I follow the instructions from the Shimano website to set the high and low limits but no matter how many times I start over i run into the same issue...It will not shift into second which can easily be fixed by using the barrel adjustment to add more tension but the issue is I have to add so much tension that the shifter will no long shift into third as there is too much tension. I can either get first and third to work or first and second but not both, any suggestions on what I may be doing wrong or what can be done differently. Beloe are the steps i am following.

-Attached derailleur so the chain guide outer plate should be directly above and parallel to the largest chainring (aprox 3mm above)
-set chain to largest cog in the back and smallest in the front
-set low limit so the chain just clears the inner plate
-attched cable to derailleur
-set chain to smallest cog in the back and largest in the front
-set upper limit so the chain just clears the outside of the cage
- set chain to larges cog in the back and middle in the front
-used barrell adjustment so the chain just clears the inner plate


Thanks

If you can get two positions, but not three, it sounds a bit like you're hooking the derailer up w/o the shifter being in its "start" position.
Pull at the wire a bit where it's handily exposed, and try a couple of downshifts. Then hook derailer up when you know the shifter isn't releasing any more wire.