just my opinion.....the arc start on the precision tig 275 is better than the 250dx. the miller has had a few problems with high frequency transformers that miller says is finally fixed. with that said, they both have nice welding output. as for the 200dx compared to the 205, the miller beats the lincoln hands down. the better adjustability of the frequency and balance make this machine the superior unit of the two. I have used all of these machines at one time or another, and usually (but not always) the choice boils down to which one will look better in your shop. as for which machine would be the best for your application, this could be a case of bigger is better, although i prefer the ability to fine tune the ac arc on the smaller inverter machines as opposed to the transformer machines.
Staying under $3000 will be hard to do w/ a new TIG welder. That price limits you to the Dynasty 200. Personally, I like the inverters because they're more portable than the transformer machines. Also, there is a lot more you can do w/ an inverter when it comes to adjusting parameters.
I think if I was in your situation, I'd try to get some more money and go w/ a 300 amp inverter WITH a water cooled torch. You can weld 1/4" aluminum w/ a gas cooled torch, but not for very long...the handle gets so hot that you can't touch it after a while! Not only that, it'll make your tungsten last a lot longer.
You might be able to find a welding supply store near you where they will let you test out different machines. That's the best way to find what's going to work for you. All the welding machine companies make good stuff, and they all make bad stuff, just like car manufacturers.