Due to chain rattle I went about adjusting the front derailleur, the L and H screws, etc. At some point I disconnected the cable, and I can't get it back on properly so that I can effectively change gears. I have to push the lever in far too much to get to second and it's impossible to get to third. Also, my tension adjusters don't seem to do anything, even after turning them almost all the way out. I feel like I've watched every video but they don't go into enough depth regarding the proper way to put on the wire.

P.S. Brand new bike and I'm a newb using the internet trying to teach myself this stuff. Thanks.

Put on middle ring.
Screw adjuster all the way in then back out 1/2 turn.
Screw in L screw far enough so that the the DER won't shift to the smallest ring. (rear on smallest cog)
Shift SHIFTER to lowest gear

With bike on stand or someone holding the rear, slowly pedal.
Back off the L screw 1/4T at a time until chain drops to smallest ring. Turn another 1/4-3/8T.
Loosen cable clamp & pull the slack out of the cable semi-firmly and reclamp.

Sometimes the routing of the wire on front derailleurs can be a bit confusing. I've been caught out a few times myself. Are you able to post a photo? Or maybe a link to a photo?

Is there a bike shop nearby? Maybe run the bike to the shop for a quick fix.

That was my first thought too:

Many front derailleurs have a little finger near the cable anchor screw. I find it counter intuitive but the shift cable is supposed to go OVER that finger. Makes a huge difference.

Stick an allen key between the seat tube and fd cage before clamping the cable. You would be effectively resetting the "low" position further to the right.

Choose an allen key thickness such that the fd clears the chain in the small ring - big cog combo.

A simple rules ror cable routing.

Route cables outside everything, so it's as far from the arm's pivot as possible.

The logic is equally simple. Adoing material costs money and adds weight. So makers don't add any useless material beyond what's needed to establish the desired cable position.

There a few rare exceptions to this, but they'll be obvious, because you can't go around them on the outside.