Hey
keyush06So for the R1 application, you should be done with your GRE latest by June/mid-july(preferably) so that the next 2 months you have more time to focus on applications only. And believe me, applications do take time. It needs a lot of work from our end especially if you are targetting top colleges. There are a number of components of an application that you will need to work on. So it's safe to have the last two months assigned for this.
And R1 v/s R2, I believe they are the same. If it's R3 then it is assumed that less no of seats will be there. So there won't be a major difference. That being said, I would always suggest applying whenever you feel that your application is strong enough.
All the best. Let me know if I can help you further.
Regards,
R