I've been in this boat very recently, so I think I have 2¢ to offer here.
Firstly, plan on your build costing $850-ish, so you've got some "wiggle-room" in your budget. $150 may seem to be a bit much for "wiggle" but you WILL run into something
unexpected, so it's best to plan on it from the beginning.
There is validation to both points that you need to buy quality or you need to buy two. A lot of the aforementioned "unexpected-something(s)" can be resolved with a warranty, for example: My Schwinn DelMar was a great deal on CL for about 1/2 the price of a new one, however the rear hub died on me, and cost me every bit of what I saved and then some having my LBS re-lace my spare hub into the rear wheel. Same goes for the engine; you get what you pay for. You can buy a 2-stoke kit from the 'Bay for $140 shipped, but keep in mind that there are reputable engine builders that charge more, but offer reliability-related enhancements and great customer service. A 4-stroke is renowned as highly reliable, but naturally costs a bit more. I've heard legend (and seen YouTube video) that a shift-kit makes a 4-stroke a very street-friendly cruiser, so it's made both my "fantasy-list" as well as in actuality.
Personally, for $1K, I think my shopping list might look like this:
~$200 7-speed Schwinn Sanctuary or Point Beach (a personal preference despite my recent hub-dud)
~$400 4-stroke HS kit
~$200 SBP shift-kit
...with enough price-shopping and a miraculous lack of the "unexpected", there might even be some left for a GhettoBike tank.
Nonetheless, that should hold little bearing as I am still very much a sooper-noob, however, I would like to finish with a nugget of knowledge that blind-sided me once I started building: Beware of killer fenders!