By the time you complete your Haedrig's Gift set, you should be at Torment V or VI at the least, especially because in order to complete the set you'll have to do a Greater Rift solo at level 20 and kill the four Keywardens and Gnomb and Zoltan Kulle at Torment IV to even get the full set.

What level should I be for torment 1?

You should start Torment 1 immediately upon reaching level 70. A significant number of class items do not drop below Torment 1, so farming below that point is a waste of time.

What level should I do Nephalem rifts?

There will be a pylon in town to start them. There's no level restriction on regular rifts, greater rifts require level 70, though. All of this requires the Reaper of Souls expansion, the base game only has the campaign.