Last night I decided to give my new bike a tune up as it was shifting slowly and the front cage was rubbing against the chain. It's a 21 speed Hybrid bike with Shimano indexed shifters. The rear derailleur adjustment went beautifully but the front derailleur... not so much. After adjusting it (lowering and changing angle) its better but second gear rubs badly on gears 1, 2, 6, & 7. If I get it to clear one side it messes something up on gear 1 or 3 usually. Most of the rubbing seems to be on the inner front part of the cage with some rubbing on the outer half of the cage when in gears 6 & 7. Is this a sign of the angle being off or is the front derailleur on my bike junk (my bike is a lower-middle end $300 model, so it's Shimano but I assume low end Shimano)? Also I assume that second gear should be able to reach gears 2-6 if not all of them... is that an incorrect assumption?
I just read this guide and I think my derailleur might be adjusted in a little too much but I haven't been near the bike to check, since finding that guide.
Any advice is appreciated,