You don't have to print the tickets any more you can show the screen of your smartphone.
Make sure you keep your phone charged.
You only need to go to the main entrance if you have want to get a special concessionary ticket which could be for a handicapped person or a child.
By far the easiest way of getting into the Alhambra for most people is the Justice Gate. (Puerta de la juticia)
There is full information about how to get there here.
https://granadamap.com/important_places/puerta_justicia
Most people could walk up the hill to the justice gate from Plaza Nueva but it is uphill.
If you don't think you can walk up the hill get on a C30 minibus. The bus stop is behine the statue at the end of Gran Via.
There is more info about these buses here You could also get on the C32 if it goes past near to where your accommodation is.
This page with information about the layout of the Alhambra will help you understand things.
https://granadainfo.com/alhambra/layout.htm
Frequently asked questions about Granada