I am very new at this and I'm trying to adjust the front derailleur correctly. Is there a certain front gear I have to be in before moving the height of the derailleur band up and down so that the outer chain guard is 1-2mm above the largest chainring? Because the videos I've watched seem to have the chain on the smallest gear but if I move it there, the outer chain guard will not line up with the biggest ring. My bike has a triple chainring.

The derailleur cage has to clear the largest chain ring--it's simple physics.
Jon

I've never seen any trick to doing it easier than the hard way:

Shift into the big ring
Decide whether you need to raise or lower the derailleur, and by how much
Shift into the small ring, so the cable is slack
Loosen the band clamp
Adjust the height, guesstimating the amount from what you saw before.
Try not to maladjust the rotation
Tighten the band clamp
Shift into the big ring
Repeat

the short answer to your question is you have to be in the small ring so the cable is slack, otherwise the cable will pull the whole derailleur when you loosen the band clamp.

Can I say 'band clamp' any more times?

This one time, in band clamp...

If you remove the cable, you can manually push the derailleur into position, then adjust the derailleur for clearance. The reconnect the cable when you're ready.

I removed the cable but the derailleur's outer chain guard doesn't line up with the largest ring. It sort of lines up in between the smallest and 2nd ring which makes it difficult to see how much room I have when it's lined up with the largest ring. Am I able to manually push the derailleur up to the 3rd cog or do I need to actually tighten the clamp and cable and shift to 3rd every time? I tried to push it but it seems like I have to put a lot of pressure to push it so I didn't want to break anything.

That's why you check it when the cable is on and you can shift it into the big ring. Try to decide, does it need to go up 1mm? down 2mm? Then try to reproduce that adjustment when the cable is slack, and check it again after it's wired up.

You can move the derailleur cage by hand with the cable detached, it's a fairly strong spring. You don't have to worry about breaking anything, just try to apply the force in about the same place the cable would be pulling, and then it's no different than the cable pulling it. Don't push way down at the end of the cage or anything.

You should be able to move it to the outer ring not unless your limiter screw for High gear is set wrong.

Thanks. I will give that a go.

Also, I'm a little confused on my left shifter. It's a lever type shifter with a lever on top that shifts it from 3-2-1 and a bottom lever that shifts from 1-2-3. This is weird to me because the right shifter's top lever shifts from 1 to a progressively harder gear all the way to 7, but the left's top lever shifts to an easier, smaller gear so they are reversed Is this right?

Yes they are reversed in terms of whether top/bottom makes it easier/slower for uphills, and which direction makes it faster/harder for downhills.

They are unified in that the big lever requires more force, and it pulls cable so that the corresponding derailleur moves the chain to the bigger cog (more teeth). The other lever releases cable so that the spring in the derailleur can allow it to fall back and move the chain to a smaller cog.

The oppositeness comes because the gear ratio is front teeth divided by rear teeth, so since rear teeth is in the denominator, more teeth means slower, while front teeth in the numerator means more teeth=faster.

I think I did it! It doesn't rub in any of the 3 gears anymore and goes up the gears easily. However, going down from 2nd to the smallest ring takes a little bit and the derailleur rubs for a few seconds before the chain goes to it. I've loosened the cable tension and I don't think that's working. Is there anything to adjust to make it go into the small ring easier?

That makes sense. Thanks for clearing it up!

I've encountered a different issue with the front derailleur. The outer guard is a little too close to the biggest chainring and the high screw adjustment doesn't move it far enough outward. Is there a way I can move it further out?

The screw doesn't move it outwards, it's a limit screw, it limits its motion outwards. If you screw it in, you will push it in. If you loosen it until it is not limiting anything anymore, then the amount it goes out will depend on how far the cable pulls it out. If you want the cable to be pulling it further out, then increase cable tension either by adjusting a fine-tuning barrel adjuster if you have one(at the shifter maybe?), or by reattaching the cable. Shift to small so the cable is slack, loosen the pinch bolt, pull a little (couple mm) cable through the pinch bolt to remove a little slack, tighten the pinch bolt again, then shift in the big ring see how it looks.