You will get lots of opinions on this subject. Here is some from a 393 owner.
Any of the big windsor strokers will give you good driveability and reliability if you choose the correct overall combination. You just need to use the right heads, intake, carb, exhaust, and camshaft for your goals. 400hp is a walk in the park with any of the larger windsor strokers.
Hopefully your vehicle is capable of handling all that power. . . . . . 400hp at the rear wheels in a vintage car is nothing but trouble if the car (and driver) are not up to the task.
If you are going to spend the money for a full kit (crank, rods, pistons), I would spring for the 408 as it is probably the best all around engine that is commonly available. Choose the one that uses small bore Chevy rods and you will have minimal clearance problems. Make sure the pistons are forged. In a street motor, a good I beam rod and a standard (non-forged) crank will be just as strong as the block and fully capable of 400+hp. A 393 would work too, but if I were to do it all again, I would have a 408.
A supposedly cheap 393 can be built using your stock rods. You buy a 3.850 stroker crank and use 302 pistons. For street usage the pistons would need to be rated at less than 8.0-1 compression in a 302. When installed in the windsor stroker, you would be pushing much, much more compression (10.1+). Stock rods should be rebuilt and I would add some good ARP rod bolts. Ultimately, by the time you get everything prepped and ready to go, you would probably have just as much $ in this combination as you would to have sprung for the full on stroker. The full on stroker would be stronger too . . . .
I prefer kits made by Scat, as they seem to have more consistent machine work. Eagle makes some good stuff, but sometimes it takes more $$ to correct some poor work on their cranks. I have heard good things about Probe too. It is best to stay away from the cheapest manufacturers, such as CAT. The stuff can be made to work, but you may have more money in it in the end than you would have if you just sprung for the better models. No matter what you get, have your machine shop go over every bit of it and be sure to have the combination balanced locally using your balancer and flywheel.
There are several good places to purchase kits. One of the old time favorites on the web is adperformance.com . Brian is well known for good prices and excellent customer service.
I mentioned that the combination is important. You need to treat the stroker as if it were a big block (which it is.) It requires somewhat more capable stuff than you would use in a 289/302/351w. You should plan on aftermarket heads, such as Vic Jr. or AFR 205's. Stockers are really not up to the task and will be a bottleneck. Keep compression below 10.5-1 to use street gas with aluminum heads, and below 9.5-1 with iron heads. As far as intakes, I like the Vic Jr., Stealth, or RPM. The Vic Jr is great at the upper RPM range (4500+). The others give you more low end torque (which is really not needed with a windsor stroker--speaking from experience.) The 15 or so lbs of torque difference between the Vic Jr and the other 2 dual planes will never be missed on the lower end.
For a street carb, use a 750dp for a stick car, 750 v.s. for an automatic should be in the ball park. Camshaft, I would recommend a custom for your combination, although you could get by nicely with something in the 236-248 duration, 550-600 lift range. For exhaust, look to make it free flowing. 1 3/4" headers and 2 1/2" exhaust would be sufficient for a 400-450hp car. You will need to buy special swap headers as 289/302 units will not even come close to filling, especially in a 65/66".
Most swap headers require that you use 66' and newer motor mounts for clearance. I was able to use the 65 mount, with a few mods. The 65' mounts lower the motor lower into the bay approximately 1".