First things first - I apologize in advance for this being a lengthy reply, but it comes as a result of about 15 years of choices, and over 40 years of planning.
Your skill set is already fine for building a Locost. It's certainly more than I started out with! Your strongest trait is the desire to actually do a build. Once you have that, the rest is "details".
In my opinion, you will need a MIG welder (preferably a "gas" model), although a budget unit will do just fine. Lots of folks have had great success with Harbor Freight brand cheap ones. I built almost all of my frame using my first 120V "El Cheapo" Italian MIG, and it came out absolutely great. I had NO experience MIG welding, so I practiced for awhile on some scrap until I was confident. Sure, I still had to grind out the odd weld I wasn't happy with along the way, but that made sure that, in the end, I was supremely confident in the ones that resulted.
One piece of advice I'd offer is to not
necessarily limit yourself to one, specific "donor". Shop around for other ideas. I started with one specific drivetrain idea, then switched to another, and another, and finally abandoned the entire idea of using any single "donor car" for my build.
While this can be a little more expensive (surprisingly, though, not a LOT more expensive), it offers a wealth of advantages. First, you're not forced to try to adapt your build to your donor parts "because you already have it in stock". A Locost isn't "like" any donor car...ergo, limiting yourself to your "donor" car can mean making a large number of rather significant compromises.
I chose to use a McSorely frame, the plans modified by Jim himself for myself & my partner-in-crime (who's building the other of the pair of cars we're working on), which is kind of a +4+2+4 design. The reason we chose that is because we wanted something that appears to be true to the original Chapman look.
I'm a bit of a traditionalist, so I chose a Ford Zetec engine, using Weber 45DCOE carbs (EFI & computer are gone!), backed up (for simplicity of build's sake) with a Ford T-5 trans & Mustang II rear axle & front suspension uprights. It all looks very "right" & true to the original concept...but big enough that a North American can actually fit in it & drive it. The original 7's were
TINY. Anyone over 5'7" and 150 lbs. need not apply. The changes we had made to our frame design allow me (at 6'2" & 190 lbs.) to fit comfortably (if snugly) into the car.
There are lots of "build diaries" here, which will aid you in making your most informed decision. Most likely, NONE of them will be exactly what you want, but there's such a wealth of truly expert experience here that you WILL find all the information you need to do a build you can be proud of.
That's one of the most rewarding things about building a Locost - it's not something you bought, or something you assembled, but something you actually built, with your own two hands, using your own ingenuity. The pride of that is something to be experienced! Mine's not even finished yet, yet when showing photos of what I've done so far simply astounds people, who simply can't believe it's possible for someone to build a car from scratch. Their wonder, and respect for the builder, is like nothing else.
I encourage you to carry on & build a Locost. It may be the one, most-defining physical accomplishment of your life, and a source of pride for the rest of your life.
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Scratch building, at continental-drift speed, a custom McSoreley-design framed, dual-Weber 45DCOE carburated, Zetec-engined, ridiculously fast money pit.
http://zetec7.webs.com/