Tony (twobjshelbys) touched on something you need to resolve at the front end of your quest. A $20K budget will not get the job done!
Unless you buy a finished car, you will have to buy the basic car, in either kit or roller form. A complete kit
less the drive train is going to approximate your $20K budget you set and then some. An engine will represent essentially another $20K and then you still have to build the kit, supply a transmission and drivetrain components.
The kit build, if you are comfortable with body panel finishing, painting, electrical and general fabrication (including welding) will work you physically and mentally. If you are not comfortable with those projects and the required skills, then you have to budget for buying them from someone else.
The paint is the obvious big buck item. If you can find it in the $5-6K you are in the hunt. Small component fabrication is easier today with 3D CAD software and CNC job shops but still stunningly expensive. I had a billet aluminum
oil manifold built at a CNC job shop for a dry sump style external wet sump pump from a 3D sketch I did. The manifold was $500, the pump was another $500. Pulleys, belts, and plumbing were several hundred more.
These cars, whether you buy them as kits or rollers and finish them or you buy them as a well built, properly sorted, quality used example are very difficult to get below ~$50 - 60K. There are lots of examples that,
'just need a little TLC', which new buyers think they can buy and cut some corners, expense-wise. That usually does not work out the way they originally thought it would.
In the end, the buyer who thought he could build the budget replica usually throws in the financial towel a few years down the road and runs a for sale ad that reads like something like this;
"Excellent condition XXXX Cobra Replica best of everything, nearly complete, must sell because _______ (fill in the blanks)." The blanks could be getting married, buying a new home, the dog bit the neighbor or any number of other outrageous excuses.
If indeed you buy the car, you will find the low budget approach caused the original owner to buy components you don't want to use. By the time you get all the incorrect 'stuff' replaced with correct 'stuff' the car is way over the economical budget you thought you could build it for. Sometimes you sell it with an ad like the one you bit for. Sometimes you finish the build wishing all the while you just went out and bought that nicely finished one way back when.
BTW buying good finished ones takes a bit of skill (usually obtained though previous ownership and building experience). The best bet for happiness is buy a roller from one of the manufacturers, buy an engine from a shop like Lykins Motorsports or Craft Engines and have an experienced installer put it all together for you.
The cost will be in the $80K to $100K+ area when you are done — depending on the roller you select. If you pick a high end car like a Kirkham you will love it to death and go by the $100K so fast it will make your head spin. If you buy a roller from ERA, SPF, FFR etc you will be in the $80K and up window depending on who you select.
There are no cheap seats left in this particular sort of project. When you think you have found one you will discover, usually after it is too late, there are additional monies required to bring the car to what you want it to be. If you forge ahead and spend the monies, there is always the buyers remorse associated with discovering this was not the smartest way to approach the project.
Bottomline, these cars have become expensive over the years. Good used examples can usually be had for $30K or so less than you would spend to build a comparable car. It will be very hard to escape these days without spending ~$50 - 60K for a quality used one and probably around $100K to build new — unless you buy a Kirkham, which are to die for replicas.
If the $20K budget is a real number you would do yourself a very big favor by not beginning the project.
Ed