With the addition of Run Customized, the run menu looks like

Python Shell
Check Module
Run Module
Run... Customized

This order resulted from Check and Run Module originally being implemented as extensions, which forced them to be below Python Shell.  The situation was similar with Format Paragraph being forced below less commonly used options on the Format menu.  It is now at the top.
Run... Customized was tacked on below, without worrying about the appropriate order for the menu..

On issue #37627, Raymond Hettinger suggested "Move the [new] menu option up by one so that the regular F5 "run" is last -- learners we having a hard time finding and mouse targeting the more commonly used regular "run" option.  The result would be

Python Shell
Check Module
Run... Customized
Run Module

I would rather make Run Module, the most commonly used option even more prominent by putting it at the top, perhaps by reversing the order.

Run Module
Run... Customized
Check Module
Python Shell

With Run Module at the top, remaining items could be ordered by logic, and to me, the above is plausible on that score, or by use, perhaps putting the second-most used at the bottom.  I suspect that this will be Run Customized.  To me, Check Module is useless, though I can imagine situation when it is not.  Python Shell is only needed when there is no shell and one does not want to make one appear by running a module.  To switch to an existing Shell, on should use the Windows menu.  Anyway, another candidate is

Run Module
Check Module
Python Shell
Run... Customized

Perhaps we should use a separator to differentiate between things that run in the shell and those that don't, e.g. as following:

Run Module
Run... Customized
Python Shell
-------------
Check Module

Run Module and Run Customized both run Check Module first.  All three involve the code in the particular editor.  Restarting Shell is not editor specific, so I see *it* as the oddball.

The proposed Run Checker #21880, would involve the editor code, might or might not Check Module first, but would not run in or involve Shell at all.  It might be a good candidate for the last position.  If it were added, I think my first option, Run Module ... Python Shell would be better.

Ah, my bad, I mixed up "Check Module" with the proposed external checkers feature.

Anyways, I'm +1 on this reordering, but have no opinion on the specifics.

+1 for the proposed reverse ordering:

Run Module
Run... Customized
Check Module
Python Shell

New changeset 14070299cdc0faf36975f0cc2d51824a9abf3db0 by Terry Jan Reedy in branch 'master':
bpo-37748: Re-order the Run menu. (GH-15115)
https://github.com/python/cpython/commit/14070299cdc0faf36975f0cc2d51824a9abf3db0

New changeset 9c95fc752c1465202df67fa894ef326c8ebb8cac by Miss Islington (bot) in branch '3.8':
bpo-37748: Re-order the Run menu. (GH-15115)
https://github.com/python/cpython/commit/9c95fc752c1465202df67fa894ef326c8ebb8cac

New changeset a96f0367d4c84ed42f8dc80c88c10f334498f36c by Miss Islington (bot) in branch '3.7':
bpo-37748: Re-order the Run menu. (GH-15115)
https://github.com/python/cpython/commit/a96f0367d4c84ed42f8dc80c88c10f334498f36c