1966 Barracuda engine swap to a 340 Six Pack

With a 4K budget,at least one of us is dreaming!

Even if you were fully experienced in this type of work. I don't mean to knock you in any way, and I'm glad you are excited, but you are building a complete new car, So you need to re-evaluate you budget. Or your time-frame.
To recap; engine will be rebuilt, and
needs the following upgrades; Transmission, TC,the rearend, cooling system,fuel system, ignition system, the $2500plus 6pac system,suspension,steering,brakes,TIREs,exhaust, and don't forget the A/C.
I'm seeing over $13,000 Canadian in parts alone. And I'm seeing over 70 hours there. So if you have to pay people that could be another $7000 Canadian. SOooo,maybe $20000Canuck-bucks.
And we haven't even talked about the mini-tubs you are gonna need, nor about the big hole in the hood you are likely gonna have to make, and the fabulous header fitment. Mo time, and mo money.
Ok so now that the shine is off the apple, What can you do with $4000 USd and whatever the buy-in on the engine is/was?
Well, first things first, the 6pac has to go on the back burner, relegated to someday. Next to go is the mini-tubs, suspension, and tires. Then if your car does not already have A/C, back-burner that too.
Then grab a stock 904 and Stock TC, and an 8.25 with at least 2.94s. Of course that means the cam has got to be down-graded. Which may lead to a compression re-adjustment. Brakes are a must, so if you currently have 9s they gotta go. I would suggest a heavier set of T-bars and a swaybar as must-haves. With the smaller cam, the current fuel and ignition systems may be OK, and so also may be the current cooling system. That just leaves the exhaust system. You gotta have one, and the sources are limited so that cost is pretty much inescapable. However with near stock output from the 340, hi-po manifolds are back on the table, and Trebleg can get you going there.
So let's see where this is going;
340 gasket set,cam and lifters,used intake and carb, used904 with TC, a used 8.25 with a new LSD and 10 inch brakes, new rear big bp wheels, used 73DBs up front, with matching bp wheels, newT-bars, newS-bar, HO Trebleg manifolds, a lil exhaust work, and probably;tires.So what's that come to? In parts,I see maybe $5000Can. Maybe $3850USd? You are going to have to learn to do the work yourself........ :)
As always, I'm wishing you the best.