For the evening visit, I'd go through the Justice Gate (the mini-shuttlebus stops there after stopping at the main entrance, and line up by 9.45. It sounds like 10 is the last entry, so the sooner you are in, the more time you'll have before they close.
For the morning visit, you could go through the Justice Gate, but when I was there several years ago, you could only get maps, information and audio guides at the main entrance. If you choose the main entrance, allow another 20-30 minutes to walk to the Nasrid Palaces. If you have large bags or backpacks, you will probably have to check them at the building near the Nasrid entrance - allow time for that since there may be a line. There are also toilets there. Expect that people with 10.30 tickets will be lining up before 10.00 so be sure not to get stuck behind a lot of people who aren't going in - you could miss your entrance time and be out of luck.
Not all of the Nasrid Palaces rooms are open for the evening visit, so you'll exit near the entrance. In daytime, the exit is somewhat far from the entrance. If you don't have to circle back to the entrance to pick up bags, visit the Alcazaba first since it's very close to the Nasrid entrance.