I'm not sure, but I sure like that wheel in the background!
What is it?
But back to your question, you can run 5/16" in both directions, or the more typical 3/8" feed line and 5/16" return.
But 5/16 is enough to feed a normal Explorer engine. If you're building a more high performance version, or plan to in the future, then running 3/8" now might save you some trouble in the future.
I won't specify the "best" way to run them at the engine, because it's been done different ways successfully. I'm sure different folks know and can offer part numbers of fittings and such.
Personally though, I think the stock lines with the braided flex line are very good and have a long life expectancy, as long you can adapt them at the other end to your fuel supply system.
It might be easier to adapt your own hose with the proper quick-connect fittings to go to the fuel rail directly.
Mine has partially utilized the factory stuff I believe, but I did not plumb it, so would have to peek back there to remind myself of what Doug did. With any luck he'll chime in with his preferred method anyway, since he's done at least three or four of these now.
Oh, and by way of a PS, is that line on the left bent up and damaged? Or is that just the way it looks? Kind'a looks kinked from here.
If it has been compromised, that might make your decision for you.
Good luck.
Paul