I'll throw in my .02.
If you zero deck the block and go with flat top 167's you can definitely pick the heads later. I would look at closed chamber heads though, and not open chamber 360 heads.
The closed chamber heads set up a better quench, and will give you better compression numbers. That will allow you to set up your compression as you want it without shaving the heads down, and should make more power.
In looking at all the heads out there, the magnum heads for a street 318 are a pretty good choice. They outflow the original 318 heads, are pretty much comparable flow wise to the 360 heads, and have closed chambers (usually around 60cc's). That will let you run around a .040 head gasket and put you close to or right at 10:1 for the compression. Yes, that's pretty much the 400hp Mopar Muscle build. And while I don't think in street tune that engine will make 400hp, I do think its a good build plan.
The nice thing about the Magnum heads is that they're everywhere, and they don't really need any work to make good power. The already have 1.92/1.62 valves and flow almost as well as a 2.02/1.60 J head, depending on who's bench numbers you look at. They also have a newer design for the chamber and ports, so some say they're more efficient than the older 360 design. The only real issue is the conversion parts, ie, you'll have to get oil through lifters and push rods, a magnum intake and the 1.6 ratio rockers. Intake choice is a little more limited, but for a street engine they have a Magnum version of the RPM air gap, which is a great intake.
302's are a good option too, as they're also closed chamber heads, but they also have the smaller 318 ports and valves. They flow well with bigger valves and a little port work, but then you need to have that work done. Without port work, magnum heads flow much better. And the 302's aren't usually as easy to find, and they tend to be more expensive if you can find them.
The only real issue with 360 heads is the open chamber design. They have larger ports and valves and flow plenty well enough in stock trim for a 318. But, the chambers can be anywhere from 65 to 70cc's, so you have to watch your compression ratio. Now, if you can find a set at 65cc's and aren't looking to be right at 10:1, they'll be fine.
As far as cams go, everyone has their own preferences. I like the Lunati Voodoo series, something like a 60402 or 60403 make good street cams. Keep in mind that if you do use magnum heads to take into account the 1.6 ratio rockers, you'll end up with more lift than advertised since all the specs are with 1.5 ratio rockers.
Realistically, getting the pistons at zero deck and setting everything up with a torque plate hone and square deck is the starting point you need. Get the compression in the 9.5 to 10:1 range and any of the above heads should put you in the mid 300 hp range with a good cam.