Double
As a writer, I always double space after a period, and as an editor I moderately prefer double spacing after a period. Anything that gives me more room to insert proofreaders' marks is a blessing.
But honest to God, no one really cares. This whole single/double space thing got started because some unknown soul tried transferring format requirements for electronic publishing to manuscript submission. Other have grabbed onto it like it's some sort of rule, when the truth is no one cares.
The manuscript itself is not going to be published, so it doesn't make a rat's behind worth of difference whether you single or double space after a period. You can triple space, if you want. Shoot, quadruple space. Then I might actually have enough space to slip in a proofreaders' mark without my glasses.
Really and truly, no editor who has a clue, who has ten percent of a clue, cares. It changes nothing. Double spaces do give me a minuscule bit of extra room to insert proofreaders' mark, but 99% of the time, I'm not even going to notice, and neither is any other editor.
I'll guarantee no editor is ever going to get mad, or reject you, or start cussing because of how many spaces you put after a period.