How to safely attach block-and-tackle to 2x8 ceiling joist(s) to handle 1000-lb load?
You want a LONG beam on TOP of the joists to spread the load over LOTS of joists, since your garage is probably not designed to have very much (if any) load on those (particularly if there is not a floor on top of them, which it sounds like.) I'd suggest 10 or 12 feet minimum so you pick up 5 or 6 joists to share the load. 16 feet would be better.

You can throw some hurricane ties at it to hold it in place. It wants to be "on edge" (if it's not square, the narrow sides should be top and bottom, since the depth of a beam is where its strength is.) If it's square, you don't really NEED to hold it in place, as it won't roll over, and gravity will hold it there just fine.

A section of chain around the beam is a good way to hold a block without depending on a bolt attachment. Lift-rated eye bolts are available, but they are fairly costly. Chain and chain accessories rated for 3000 or more pounds are easy to come by. But make sure every element is rated for (several times) the load you want to carry. Do NOT use "1000 lb rated" parts if you actually want to lift 1000 lbs - always add a safety factor.