The 14-euro Alhambra General ticket is the one that covers a daytime visit to all parts of the very large complex. It's nice to also see the Nasrid Palaces at night, but that isn't essential. Just buying the "Gardens, Generalife and Alcazaba" ticket would be a mistake; it omits the Nasrid Palaces, which are the most beautiful part of the complex by far. That's the part that can sell out well ahead of time. There's an extra charge for the audio guide, which I thought was very much worth it.
The Dobla de Oro ticket gives the same Alhambra access as the Alhambra General ticket and also covers some secondary sights. It's our usual suggestion if someone finds the Alhambra General tickets sold out for the day he or she needs. A short-term visitor is unlikely to have time to get to all those secondary sights, and there are other places in town not covered by the Dobla de Oro ticket, some of which might be a higher priority. Individual tickets to most of the secondary sights are quite inexpensive, so the savings from the Dobla de Oro ticket are not large.
I believe hotels in Granada are generally very reasonably priced. I think you can find something nice for much, much less than that eye-popping parador rate. If you give us your nightly hotel budget in euros and tell us how many people are in your group and how many rooms you'll need, we may be able to help more. In the meantime, take a look at booking.com.