Welcome to the site Sterling, the home of Datsun lore & plenty of good people to know.

If you include a basic location in your profile it will help a lot since you are presenting us with a bit of a puzzle.

With words like "Datsun Fastback Coupe" & "tranny" it sounds like you are in either the US or Canada, but the eBay engines in the photo below are in Queensland.
The 'fastback' description was used on North American cars I believe, but not on Japanese or Aussie models as it is un-necessary since all of the coupes were of the 'fastback' type.

You also forgot to mention just what model of Datsun Fastback Coupe that you have, 1000/B10, 1200/B110, 120Y/B210 or Sunny/B310/210.

The A15 engine should physically bolt directly into the 1974 & later models [120Y/B210 & Sunny/210] but require a little more work to fit to the earlier cars as the engine mounts are in a slightly different place & the alternator is on the opposite side of the engine to the earlier ones.

The original trans that came behind the A10, 1200, or A12 engines was a beautifull little design ideally suited to these engines, but was not used behind the A15 because it was deemed to be not quite up to specs in the strength department, so a larger gearbox was used.
If you use the smaller gearbox, then treat it with respect & it will serve well, but treat it badly & you will be pushing the car home.