You have what looks to be a 302ci service replacement engine for a 67 z28. There is no way to know if that is what it started life as, especially now that it is .030 over and rebuilt, but it is by no definition a bad engine. Those pistons were used to give 12.5:1 compression with 64cc heads, and I suspect that your engine has had the 882 heads swapped on to lower compression for pump gas. With those pistons, a zero deck, and .040" head gaskets, you should have right at 10:1 compression.
That block is a 4" bore casting, and according to some sources it has thicker than normal cylinder walls. I have one dated for 62, and my machine shop did mention that it's walls were thicker than most late model 350's that they'd sonic checked. All of the sites list it as a small journal 327, but that casting pops up on ebay as a CE 350 from time to time, and i think there are even a few cases of CE 302's using that block.
As for doing a 383 kit, you can buy another crank for a small journal 383 build, or you can open that block up to large journal main saddles (GM did this on some service engines). I wouldn't do either of those though, getting another 350 block would probably cheaper than either of those approaches. If you really want to stroke that engine, you can use a small journal 327 crank and build a 331 cubic inch engine. I'd use flat tops, vortec heads, and a small solid lifter cam for a street build that would run on pump gas, provide the grunt that your truck needs down low, and allow you to run it up high the way early 327's did. That probably wouldn't work as well as 383 in that c-10, but you would definately have something to talk about as opposed to the dime-a-dozen cheap 383 builds that are in the older pickups.
You can also leave it as a 306, but you'll have to think long and hard about the cam choice to get it to work well in a truck. It will certainly breathe better than a truck motor 305, so that's not to say that it can't work in a truck, but that engine is definately out of it's element between the fenders of a fullsize.
What I'd do with it is just freshen it up with new rings and bearings, possibly a hone job, put a set of fresh double humps back on, and stick one of these cams in it:
(those are the new copies of both of the GM racing grinds, -140 is easier on the valvetrain than -754 is)
Put it on ebay or craigslist as a hopped up CE 302 and it will sell, then you can use that cash toward your 383 build.