The only issue with a .040 over 340 is that unless its a fresh hone you'll have to go to .060" for a rebuild. That shouldn't be a problem, especially for a street engine, but you'd probably want to have it sonic checked to be sure you won't run out of cylinder wall. The other thing is your piston selection for a .060 over 340 is pretty narrow unless you spring for forged pistons.
I bought my 340 .030 over, and had to go to .060 over because of the condition of the cylinder walls. If its rough (rusty, gouged, pitted etc) you may want to pass on it, it might not clean up at .060. I actually didn't think mine looked all that bad, and was hoping for .040 over when I brought it to the machinist.
Is it a complete engine with heads for $500 or $550? That's a REALLY good price if it is. Most of the complete engine, 340 cores I see go for around $1k, although thats usually for a standard or no more than .030 over bore (although I wouldn't pay that much). If its just a bare .040 over block, its pricey. I bought my '68 340 as a short block (block, mains, forged crank, rods) for under $300, and that was over a year ago. That was a pretty good deal though.