Weather forecast for this topic is flurries! As in the responses that will come in.
My answer: Depends on what parts of the engine were rebuilt. Complete top to bottom? Break it in with dino oil for 500 miles, then switch over to a 5W-30 synth, such as Mobil-1. Stick to a quality oil filter such as K&N or Mobil-1. (all FRAM filters are )
I usually dump the first batch of dino oil after 75-100 miles if its loaded up with moly from flat tappet cam prelube then another filter and a second batch of dino until I hit 500 miles then switch to Mobil 1.
Now those newfangled roller cams don't need the break in so I would do like the factory does and go Mobil 1 from the get go.
Initial mineral oil for breaking-in a total rebuild engine should be:
1) 20 - 25 minutes (engine break-in, and perhaps some initial tuning to get the engine to idle)
2) Change oil with fresh mineral oil, and continue using it for approximately 500 miles (those are easy miles too. Don't take it to the track or get on it too much. Keep it below 4,000 rpm).
3) After 500 miles, switch to synthetic.
I know that a lot of us here do not agree on the benefits of synthetic oil versus mineral oil, and I can only tell you what my experience has been with my motors, and my L81 block only needed a +0.020" boring. The crank was immaculate. All the original components except pistons were reused. I find synthetic oil more forgiving than mineral oil. When in college, I changed the oil every 8k miles (at 5 dollars a quart, I could only manage oil changes with that spread in between). All in all, my faith in synthetic oil is anecdotal at best, though -I have no facts to show for it. Just educated guesses. Aircraft engines have used synthetic oil since before I started working on them.