I'll answer for myself. I do TSGs because it is fun to play the same map with others, be able to compare plays, but mostly it is a learning experience and the most important things i would like to see are :
1) Milestones. When did people get education or universites or when they built or researched key elements of the victory condition. Mainly as a basis for a more in depth comparison than a simple win time. (Essential to know where you are being slow and where to improve.)
2) General strategy. As in "I plan to make 4 cities, focus on bottom of tech tree, and get all GS generating wonders". Maybe the things you are trying / experimenting with, as in "getting my first scientist as soon as possible by making oracle and hanging gardens for the free garden."
3) Specific play details, as in build orders, research orders, RNG elements (tech from ruin, enemy army getting stuck), specific decisions and the logic behind. Mostly this shows how the initial strategy changed because of the map or what happened in the game.
To be more specific :
Opening actions :
- General strategy you plan to use, if any. Exemple : early domination diplomatic win, with honor and liberty, aiming for a turn 200 win.
- Build order of capitol until at least the settlers. Most important is turn GL and NC are finished, when exactly the settlers were made, and when the workers were built / stolen.
- Research path up to Education at least. What is the most interesting is what techs you chose to delay writing for, and what techs you went for after. (Choices between sea techs and land techs for coastal cities for exemple can be key.)
- If there was early agression, what units were build and lost. On which turn the first city was captured would also be good to know.
After actions :
- Turns key researchs were completed.
- Which wonders were made, when.
- Possibly cities size at fixed points in time, like capitol size at turn 100 and 200. Size at every 50 turns from start would be ideal but probably too much to ask.
- Mention of any bribes.
- What mistakes you made. What would you do differently if you started over.
- Policy choices if not standard tradition -> patronage -> rationalism.
- Religious choices.