Why did they travel back to various time periods to obtain the Infinity Stones...

An excellent point, go back to the day before he destroyed them, or a few days after he completed his mission. I guess it wouldn't have made for much of a film though if they'd done it that way.

They needed to get the stones when they were apart and not working together. Since Thanos would have the stones in 2018, he would have used the stones to sense them the minute they showed up and stop them.