That Lincoln is a good choice and I would not be afraid to flux it only. I have done it on my jeep frame, body, tractor implements, tractor itself, built two trailers etc.
I would suggest to get a welder, read up and start welding, you will see yourself if you have it good neough for the frame.
For$200 I would get a welder, you will be using it again and again and every learned skill is a good thing.