For the first time x at the first time: Qual é a diferença?

Boa tarde

Estou em dúvida de como usar "for the first time X at the first time".

Exemplos: At the...time:
At the first time I've chosen the right way.

At the second time I've chosen a wrong way.

At the third time I've done very well job.

Exemplos: For the...time:
For the first time I've chosen the right way.

For the second time time I've chosen a wrong way.

For the third time I've done very well the job.

Muda o sentido usar "for the...time" ou "at the....time", ou está errado o uso em algum deles?