The HF unit would work excellent on a Lincoln Idealarc 250 AC/DC or a Miller Dialarc 250 AC/DC. They sell used from about $200 up to around $800. The Idealarc is a better machine than the Miller but The Miller is still good. Most used Miller, Lincoln, Hobart, Linde and Airco are good TIG machines but you need to be able to try them out. A Lincoln Square Wave TIG 175 would be a good starter machine. Lincoln might have a 185 too but not sure. A Square wave TIG 225 is newer but a good machine. Lanse has one. A Square Wave TIG 255 with digital controls is a good machine if the panel isn't fried. I bought one new and really liked it. The problem with the digital control was that people would go to turn their heat up and poke the hot tungsten through the control panel. A Miller Syncro Wave 250 is a good machine too. I think Miller made a smaller TIG welder in the 175/185 amp class as well. If you can find a Miller Dynasty in your price range, they are an excellent TIG welder but not the best for stick. Puddles has a Dynasty 300.
You might want to see if there is a Red-D-Arc near you. They are the largest welder rental outfit in N. America and sell used machines with a 90 day warranty. They will even load test machines and let you try them out. Bigger welding supplies or repair shops may be able to put you in touch with welding shops or welders upgrading to newer machines and wanting to sell their old machine(s).