Hi Rowena
Lombok is essentially a small island with a very big volcano. Anywhere near an active volcano will have beaches affected by it, and so you will get black or grey sand. The sand on the beach in Kelui is the same as Senggigi, if anything being slightly closer to Rinjani, it is darker.
That being said, it is not dark because it is dirty. The sand is as clean as a white sand beach. It is not muddy and the water is clear.
If you want white sand you have to go a long way from the volcano, which means southern Lombok. The sand on the beaches is white, and the water very clear due to the sea grass beds there. Alternatively, most of the gilis (being coral attols) have white sand beaches.
What Kelui has going for it is that it is quieter and you will be left alone more on the beach there. Jeeva Kelui is having a soft opening soon - this is a revamp of a hotel that has been closed for years, and it is great to see that property open again. They are offering some good opening specials, so it would be a good opportunity to get a nice room for a price a lot less than what you will pay next year. Kelui is a bit out of Senggigi. Even some of the local bemos don't go out that far, so you will mostly need to use taxis to get into Senggigi.
If you haven't booked, you are running out of options anyway as August is very busy and many places are already fully booked.
Re the gilis, Gili T has more entertainment, restaurants etc. Meno is the place to go if you like it quiet. My personal preference is always not to move around too much - I prefer to get somewhere and unpack and stay a few nights rather than constantly packing and unpacking, checking in and out, and losing a day of holiday moving from one place to the next. So my advice is always pick a place and do trips from there. If you stay on any of the 3 gilis it is easy to get a boat over to one of the other islands.