Projects Which heads would be best for a performance 318 (318, 340 or 360?)

You can probably get another 20% of HP out of the stock heads with port matching, mild porting and 3 angle valve job. Later Chrysler products had some sloppy head castings, in many cases just cleaning them up is a big improvement. Just match the ports to the gaskets and clean up the castings, slim down the valve guide area.

 

The thing is that if you are willing to fuel larger cubic inches say a 440 it’s easy enough to build 400 to 550 ft pounds of torque between 2500 and 6500, 525 hp at 6200 rpm with later 452 iron heads that are blended with the mopar templates and port matched, a decent cam intake and 850 carb. Drop the numbers by 100 and you can do the same thing with a 360 with X or J heads.
You can have good torque at 2500 to 3000 rpm and make good hp numbers with iron heads, 9.5 compression and a cam with 248 to 260 or so duration @ 50 .570 lift. A 3400 to 3800 converter for the street or 4500 for race only. This combo will run on regular gas and be fun as hell on the streets or track.
This thinking isn’t limited to mopars it worked on my 289 only better because of the aluminum heads. 292.** CID with 400 ft pounds of torque at 2900 rpm, that’s 90 percent of the torque curve! The max horsepower power is at 6300, 455hp all these numbers are at the crank and are great for ordering torque converters and gears, the Ford has a c4 and 3.73 and the Mopar will have 4.11 for the street.
Just a note that I still prefer solid flat tappet cams for the reliability and simplicity.
The duration I use is a push according to the cam company, they want a full point more but the dyno doesn’t lie, I advance the cam 2 to 3 degrees initially to cover the chain stretch witch happens fairly quick.

 

I see the drag racers and the speed shop believers have arrived.
What most of you are proposing is not even close to low budget, and much of it just isn't very street friendly. Most street playing events are way shorter then a 1/4 mile, and seldom see the rpm range exceed 4500 rpm, both of which are required for most speed shop performance parts and thought processes to work.
I've played this game for a long time. In the Mopar world, you don't just pull a 318 and bolt a 440 back in its place, there is a lot of other stuff that has to change along with changing to the big block. If your plan is to build a screaming big HP Mopar for max performance, the 318 is not the best option to start with, but if the 318 is already there, and you just want to add some more street kick to a still healthy 318, the simple things I have already covered will do the trick without breaking the bank.

The Op had a 56 Dodge with an LA 318, in stock form, and is on a tight budget. He was looking for "better" street performance. He was not building a street racer. He was not even sure what transmission was in the car.

 

@Kerrynzl posted this link for a 318.
Quite an improvement and not costly.
https://www.hotrod.com/articles/mopp-0312-318-long-block-bolt-ons/

 

I built a 360 for myy 41 Plymouth and it hauls! Did a nice compression bump on it and I wouldn't want more in this car. After a bit of tuning, I get 18 mag on the road with OD and a 3:55 gear. Tires are 225/70R15.