My advice for what it is worth comes from my first car and what I am doing now for my second. I knew I wanted a FED but that was about as far as I went. What you want to do with it class wise and ET makes a huge difference. And if you are like most of us you may just change your mind as you go.
I helped a local team that ran JR fuel and learned so much from them and other racers, and a large part of it was what not to do.
I bought a roller very cheap and very old. Paid someone to back half the car who was a very good welder but knew squat about drag cars. I got lucky and knew just enough to get a car done that was safe and not too ugly. My initial thought included a radiator, water pump, battery, and bracket racing. Then after getting involved with the JR fuel guys I went simple, light, and for the time fast (for me anyway). I built as much as I could in the way of small fabricated parts, but as I did not own a TIG or the know how to use it. Mild steel was never even a thought as you can get it done, but if you ever intend to go faster or resell it you are stuck. I certainly understand the thought of paying out small money several times as opposed to cutting one big check. If you start too bare it will nickle and dime you to death. My chassis came with a good 8 3/4 rear. $1000 later it had new guts in it and was usable to the power levels I wanted. I did not keep count of the money of the 3 years or so it took to finish, but I bet I was in it for $10k 13 years ago and the car was not competitive. Lots of trades and deals with only the safety equipment purchased new.
Had a little on track accident and bent that one and parked it.
Fast forward to now. I still cant TIG weld and have spent enough money with other shops to buy a nice welder and learn. I got lucky and ran into a local racer with a FED on a jig in his shop now and he offered to help me with a new one. I will use his bender, jig, and he will help with the welding. I will use all my old hard parts and just use his shop for the chassis itself. It is important to me that someone with experience weld this up as my life depends on it. I can handle all the little stuff like shifter bracket, body, etc.
For my situation a kit would be great, except I have the rear, and the front axle and I can buy just the tube and a few other pieces. While I love the fabrication there are a few parts that I will buy ready made, like the motor plate, rear end uprights, and the uprights next to the motor that allow cables to pass through. (probably from Parks)
I admire you for wanting to start from scratch, but a kit or a roller would be a better start. And as harsh as the other advice sounded you really need to get out and learn more before you start. It gets real expensive to do it twice.
Good luck however you do it, keep asking questions.