Since the finished plane will be in the weather any time you take it out I think building it under real world conditions should work fine. In Texas it is too hot to be in the garage for most of the year but that is where my planes are kept once they are finished. I use a spare bedroom as my shop.

Between RCKen's thread and the Airfield Models site I think you have a pretty good idea of what you need. You do not need a ton of power tools to build an LT-40, and most of the things you do need can be picked up gradually.

I think a Dremel type rotary tool with a flexible shaft is extremely good to have. Mine is Black & Decker brand. I bought an IV pole from a medical supply company to hang it. Height is adjustable and the wheels make it very portable.

Over the course of several years I bought a drill press, disc/belt sander, band saw, and scroll saw. All of my bench mounted power tools are the Ryobi and Delta models that cost about $100 at Home Depot. I have used the sander much more than the others.