340 or 360???

The 360 is definitely the cheaper and easier way to go. A 340 will be hard to find, expensive, and even more expensive to build as noted already.

The 360 is a great engine and very common, easy to find parts for, and will make just as much if not more power. As far as running or build it yourself, it depends on what your plans are for the car. If you want it running fast, don't have much cash or don't have any big race plans, finding a running 360 isn't a bad way to go. Be sure to inspect the engine as best as you can, preferably hearing it run and checking compression and the like. Ultimately, you won't know much about the engine internals, so when it comes to making performance modifications you'll want to keep it pretty mild. But not a bad way to go for a driver-level engine.

If you're looking for big horsepower or have more cash on hand, build it yourself. That way you know exactly what you've got and what its capable of. You should also know its in for the long haul, as opposed to a runner that you don't know the history on.

But I've seen complete, running 360's for under $500, a rebuild will probably cost you at least $3,000 just for a "stock" rebuild, more for high horsepower.

Ultimately your budget and plans for the car will probably make the decisions for you.