Second conditional

Hello. I just show you the result of what I have studied on the use of the type second conditional whether my understanding is right or not.

I have learned a type 2 conditional and I think I have understood it very well. For example.

If I lived in a big city, I would go out every night. Do I live in a big city? No, right now I live in a small town. I just want to imagine something different. I want to pretend that I live in a big city.

Now in the following sentences, I will say the same thing as above.

If I won this race, I would buy a big house. Do I win this race? No, I don't win this race. I just pretend that I win this race.

If I referred to the team, I would call them as X. Do I refer to the team? No, now I don't refer to the team. I just pretend that I refer to the team.

Yes, you’ve certainly got the general idea. But the last of those would probably be expressed slightly differently; for example as:

Thank you. Is it possible we use type 1 conditional as well?

If I win this race today, I will buy a big house.
If I won this race today, I would buy a big house

Thank you. Which one should I choose between both sentences?
If I win this race today, I will buy a big house. Or
If I won this race today, I would buy a big house.

Because they show the future, so it's a difficult choise for me to determine.