Most affordable and best aren't usually in the same sentence but for aluminum you need AC current and high frequency. There are inverter based units and conventional transformer/rectifier machines which require a little different set up from one another. In a new machine, you're looking around $1800 to about $2500 for a basic AC/DC TIG set up. The price can go up substantially depending on how much capacity you need and other features.
Inverters use a lot less power. Miller has a TIG only Diversion 180 inverter for around $1800 and if you want a TIG and stick machine you could up to a Syncrowave 200 or something like a Lincoln Precision TIG 225 for around $2500. Lanse in the tool talk forum has a precision TIG 225. You could also go to a Dynasty 200 Miller inverter for a little more. There are a lot of good older TIG welders too you could consider. If you see something, post it on here in the tool talk forum and there are several welders that can advice you if it's worth considering. TIG aluminum takes a lot of practice but if you can master it, it will make beautiful looking welds.