I have been using a Miller Dynasty 200 for aluminum TIG. It is perfect for the job you describe. Even with .125" thickness I would recommend strongly that you get a water cooled torch and cooler. Sometimes decent Miller coolers are available on EBAY. I use a CKWorldwide torch (17 series) rated for 300 amps for just about everything. A light torch (water cooled) will save your wrists. If the parts will be anodized, 5356 is the t=filler metal I use. It anodizes the same as the base metal. Also, invest in a decent TIG electrode grinder. I use 2% Lanthanated (blue), ground to a blunted point. With an inverter welder with square wave the electrodes do not ball like the older style welders do. When I have a big job I like to grind a bunch of electrodes and swap them quickly when needed. Then grind them all later at one time. Be careful of tungsten dust from the grinder. It is insidious. Look with a strong light near the grinder when pointing, and you will see a cloud of tungsten particles far from the actual grinders. a vacuum cleaner with hepa filter and/or a P100 dust mask are good things.
I use 1/8" tungsten almost exclusively these days for almost any thickness. for your job, 3/32" electrodes would be fine and are less expensive. I use gas lenses almost all the time for aluminum. You can get the nozzles in clear glass, which can be helpful. Weldingtipsandtricks on youtube has a ton of videos on using different nozzles and welding aluminum. You can also get stubby hardware for the torch, which might help, as it is lighter and smaller.
It is very important that the base metal be clean. Really clean. So some thought on prepping the parts efficiently might be a good idea. A stainless rotary wire brush followed by an acetone wipe works well for me. I would also recommend spending some time to build fixtures to hold the parts that position them rigidly in a position that allows easy welding is very valuable. Having a way to support the wrist might be good if you are doing a lot of these. There are actual support fixtures that you can buy which look pretty nice.
THere are MANY reasons to get a good inverter welder. Having frequency control changes the arc "force" and makes it easy to dial in the welder for the best weld in any situation. I tend to use 50 Hz for big, thick joints where I need to heat up a wider area, while 200 Hz is great for getting tight, like in corners. Your mileage may vary!
Given that you will be welding a lot, I recommend an industrial class welder like the Dynasty series. I believe the Dynasty 280 is what replaced the Dynasty 200. I have both the Miller Dynasty 200 and also a Primeweld 225. The Primeweld was around $800, while the Dynasty is $4000+. For a professional job I would buy the Dynasty. The Primeweld does ok, but just doesn't compare to the Dynasty in feel or beefiness. You will want good duty cycle too. You MAY be ok running a Dynasty class machine off 115 VAC (they autolink to whatever power you feed them-NICE!). I run mine on 240 VAC single phase, 30 amp breaker. Works fine even at full throttle.
In case it is of any use, I have had good experiences with Weldmonger.com (Jody from weldingtipsandtricks's store or arc-zone.com (great for consumables, torches, etc.).
Finally, I upgraded recently from the old Miller elite auto darkening helmet to the new clear view digital helmet. It is SO much nicer. The vision is very clear and colors are much better. Well worth the investment for a job like you describe.
I am sure you know most of this, but it is what I have to offer. I hope you have a good time with the job. You might try reaching out to Jody at weldingtipsandtricks.com directly and getting his thoughts on how to do the job efficiently. He is a really nice guy and very approachable. And a font of really useful knowledge.
All the best,
Michael