I would get the Hobart 140. I have one, its nice. It let's you change the wire speed which is what controls the amperage. The 125 doesn't. Wire feed control and amperage control is pretty essential if you want to do serious welding.
A chop saw with a metal cutting blade is best. An angle grinder with cutoff wheel would be second best, then a reciprocating saw, then the good ol' hack saw.
A welder able to do the thicknesses you are wanting. A hobart 140 will do it just fine.
If you use round tube, then you will need a tube bender (not to be confused with a pipe bender. The difference is a tube bender wraps the tube around a die and the pipe bender pushes on the pipe to bend it, it looks like a bow and arrow when in use. Pipe bender is likely to kink the tube and not fit in the tool right, and takes a lot of extra work to use on tube. A tube bender is expensive...) You will also need a tube notcher. This is basically a device that holds your tube at an angle you want, and then you use a drill or drill press and a hole saw of the diameter you are going to connect this tube to and cut a circular hole in the end. This mates the tube to the one you wish to weld it to properly.
You will also need measuring devices like a tape measure, a good carpenters square (one of the big ones, helps to keep big pieces square) clamps, LOTS of clamps. A magnetic protractor, a level.
An angle grinder with a grinding wheel and a flap sander wheel is also quite invaluable. The sander wheel is great for cleaning metal up for welding.
A drill, preferably a drill press (much preferably). Ideally you would want one that can get down to at least 300 rpm. A drill press will give you much more control over the bit, will ensure your holes are square, its just better. You will need this for drilling mounting holes in brackets for things like engine mount plates, weight saver holes, and a multitude of other things. A drill press is invaluable. And remember, the bigger the bit, the lower the rpm and cutting fluid. Investing in a set of cobalt drill bits is also wise. The TiN bits are ok, but not as good as the cobalt bits.