According to me, the area of the Villa is maybe the most important thing that you need to concern about. If you prefer to relax, to do party all the nights, to surf all morning… the area will change. For example, Ubud is the perfect destination to be in the middle of the forest, enjoy the temples and rice terraces. A contrario, in Seminyak you will find night clubs, bars, gourmet restaurants…
Secondly, the swimming pool is important but not indispensable. You will have more comfort if you have one, but you can easily do without it. I recommend you rent a villa with it on Bali Je T’aime to enjoy in the better way your holidays in Bali.
The value of the villa is important . In fact, the advantage of renting villa is greater privacy than hotel. If you are many people, the price will be the same as an hotel room but you will have a better comfort place to live. You will are in capacity to cook, invite people in your Villa etc… you have more freedom.
Each region/Villa gives you something different, choose yours!