Need expert advice on power supply circuits

I need some expert advice on a power supply circuit. Normally I would have asked my friend who was an electronic wiz, but he's just passed away this year so I need a new electronic expert. I know this is probably a lot to ask, but I figured there might be some kind soul who might lend a little of their time. I would gladly exchange what knowledge I have on other subjects such as AutoCAD, Linux, programming, etc.

I want to make a power supply circuit for a foam cutter and I've been researching them on the Internet, but I don't know enough about electronics to judge which one would be best and if any of them could be modified (safely) to fit some of the parts I already have. My skills are limited to soldering and following a good set of instructions, not design.

I've found these different designs:

From the sites I've read many recommend that you do not use nichrome

wire. So I have some stainless steel wire (0.020in DIA) left over from a different project. I have no idea what ohms/foot rating this wire has. Also, I have a working transformer that is 120V input and

My questions are:

1. Which design do you think would give the best control of the wire temperature?
2. Can any of these designs work with the wire and transformer that I already have? If so what changes to the components (if any) would be required?

Thanks in advance Brian