Awesome! Can you walk chew gum and juggle at the same time? IF so, you will like TIG welding. All this is pretty much my own opinion below and I never have been taught any welding classes.
Do you have a foot pedal? I learned to TIG weld first (don't ask why, I don't even know why). As soon as I started MIG welding, I almost immediately stopped TIG welding everything, and just TIG weld stainless every now and again.
One thing that really helped me was Jody at weldingtipsandtricks.com, because he loves to tig weld, and does a great job at teaching you how to do it. I wouldn't worry about looks just yet, but would be very very conscientious about how to hold your tig torch properly, and how to properly feed the filler wire. My old swimming coach always said practice does not make perfect. Practice makes permanent.
Filler wire: Most of the time I'm using either 3/32 or 1/16" wire, and occasionally will bust out the 1/8" for thick stuff. amperage aside, the wire acts as a heat sink and how much you push vs dab will affect weld puddle size, and weld build up. Learning to feed the wire consistently stopping to readjust is very important.
Amperage Usually, I set the max amperage to 20% above the 'recommended' amperage that the thickness counts for. You can push pedal down a little extra to get full penetration, and back off once you get your rhythm down.
TIG Finger If you are going to be welding any long beads, id get one of these, keeps your fingers from melting off to get the perfect bead.
Since you have the square wave, you are basically going to get excellent penetration and excellent looking welds once you get the basics down if you can set it up to pulse. I wouldn't worry about looks though, once you get the weld penetration and rhythm down, the look will come naturally.
Tack welding Sucks so bad when tig welding. You are most susceptible to metal warping and shrinkage when first learning to tig weld. You probably already know this, but tacks are even more important when TIG welding ( in my opinion). Since you are getting excellent penetration and if you go slow, it just really shrinks things up vs MIG.
Blow/Burn Through was my biggest problem till I got a foot pedal, and I thought wow i was an idiot for doing this for so long without a foot pedal, but it (not having a pedal) did teach me to weld fast when I had the right amps up. After i got a foot pedal, the welds immediately improved, and I was able to finish welds with the right amount of build up, quality was night and day.
Welding tubing one thing i found out (hard way) was that if you weld too slow or have tubing heated too much, when you go to seal the last bit of a fishmouth, the rapidly expanding gasses (esp if you are getting full penetration) will blow open the metal at the final puddle where it closes up the entire section to be air tight. You can avoid this by letting the weld cool completely with just a little bit of weld left to do, then hurry and weld it up before the rest of the tubing expands. Some people drill a tiny hole in the tubing, to let it all escape, then weld the tiny hole at the end.
Fitment Its much harder (actually not really but it can be) to fill a gap when TIG welding vs MIG welding. Its FASTER to fill a big gap mig welding than with tig, but if you are good enough at adding metal, you wont make a giant booger of a weld with TIG welding a large gap vs MIG, it just takes some finesse. So with shrinking, tack welding and all that in mind, TIG welding is best done on metal with excellent fitment.
Also, just one word of caution the electrodes (doesnt really matter which ones - I use lanthanated because you dont have to keep track it works on AC/DC etc) they are slightly radioactive ceriated has cesium, lanthanated has lanthanum, etc etc. When you grind them, be sure to wear a respirator and wash hands. If possible do it in a spot where you can keep the dust down. The thing with radiation is that its not that bad when it gets on yoru fingers and whatnot, but the dust and particles if inhaled (or accidentally injested - itchy nose rub etc) can do serious damage when inside your body. Also, if you pick up welding stainless steel, you will be exposing yourself to hexavalent chromium, which is a confirmed human carcinogen (lung cancer). Again, its not harmful if you get it on yoru skin, and most of the risk comes from inhalation, or accidental injestion. Would be great to have a decent half face respirator with p100 cartridges that fits under your mask. I work in chemical sampling and ocassionally hear/see health effects of hex chrome. One story that always stands out to me is that a stainless steel shop owner died of lung cancer because he never wore a respirator, always working around stainless. Mild steel is not a concern, stainless is the worst, and aluminum is worse than steel, but not as bad as aluminum.