The middle would be the most logical. Or just pick one. The number is arbitrary anyway

On average I suppose, and of course there's more than just the sun's position to think of. You also want to be in sync with neighboring countries to make sure people don't have to change their clock every time they cross a border.
For where I live, summertime puts the sun at it's highest point at around 13:20 while wintertime is 12:20. My country (Netherlands) is small enough not to have any significant difference between east and west.
But when you look over the wider timezone:

|Location | Wintertime | Summertime | |

|

|

| | Fisterra, Spain (most western) | 13:20 | 14:20 | | Paris | 12:34 | 13:34 | | Rome | 11:53 | 12:53 | | Berlin | 11:50 | 12:50 | | Warsaw | 11:23 | 12:23 | | Nowosady, Poland (most eastern) | 11:09 | 12:09 |
| Vadsø, Norway (even more eastern) | 10:44 | 11:44 |

I took those most eastern and western as an estimate, but the difference would be negligible with other nearby towns. Time of highest point is for today.

It's a big timezone when you look at the differences. During summer time the most extreme differences from sun's highest point would be between +00:09 - +02:20 hours. For wintertime it would be -00:51 - +1:20 hours, with the average much closer to noon. So yes, for my timezone, I would say wintertime is the best choice if you want noon to match the sun's highest point.

Oh no... see what you did, you brought out the nerd in me :)

edit
So I just noticed Norway has that little strip even further to the east. To make it completely fair, if you take Vadsø in account, the difference would be -00:16 - +02:20 to -01:16 - +01:20 hours. With winter time noon, on average, most closely in sync with the highest point of the sun.