I have been fortunate enough to have visited all 3 in the last 2 years; and staying at Starwood properties (with the exception of Moorea where there aren't any). I don't think there is any one right answer for your question since there is no one overall winner for what you are looking for. Some areas are better than others, but weaker in other categories.
Affordable hotel or bure/hut?
None of these are affordable destinations.
5 nights, 1000-1500 USD Budget for 1 adult,, Budget includes food and optionals? Does Not include RT airfare
Are we talking bout per night? ? Or the whole thing? Unless you are using Cash and Points, or points outright, you're going to end up spending $300-$400 per night on accommodation. I did find the St Regis Mauritius to be excellent value on Cash and Points availability if you can find it. The Sheraton Tokoriki, Fiji has good upgrade potential using suite night awards as you can upgrade into the highest category of room.
under $150 night includes pool, and meals, option to to buy food, snacks and water at store?
There are some resorts in Moorea and Mauritus where if you have your own transportation (ie rental car: Mauritius, or rental pedal bike: Moorea) where you can ride to the store and self cater. Most of the good stuff in FIJI in terms of SPG is out at the Sheraton Tokiriki, which is a boat ride away with no store availability as it is on a semi private island.
-Not interested in paying $25 US Dollars for each meal!
I don't think you are going to find any resorts that offer on resort dining lower than this price point. You may get away with dining off resort at Denaru in Fiji at a local pub or Hard Rock Cafe lower than $25 but I found the mainland Nadi / Denaru area to be really lacking in a nice beach. Not worth a trip soley to Denaru to see a man made artificial beach in my humble opinion.
-Not interested in hanging out with a bunch of tourists, more interested in the culture i'm visiting, not tourism!
I'd recommend Mauritius and Moorea over Fiji in this case. Fiji has excellent culture, but it's tough to intermix the two if you are on an outer island (where the best beaches are). At least with Mauritius and Moorea you can easily scoot off resort as needed.
-Water treated on these islands safe to drink water
I'd stick to bottled water in all locations. It's cheap and easy.
-safety issues?
This is wholly subjective. All are safe; despite occasional incidents to the contrary.
-Humidity, low, medium, or high? (Sept or October)
I can't comment on this. All are fairly humid. You might get better accuracy comparing a guidebook of the climates.
-Able to buy food at store, or only can purchase all inclusive with Hotel or Bure?
Most of the better beach / resort experiences in Fiji are on the inner . outer islands. This means that you'd have to stock up before travelling on a boat out there. You can access stores fairly easily in Papeete and Mauritius if you have your own transport.
-Cautions for not getting sunburned, happened only once!
All of those are in the Southern Hemisphere where there is less o zone. I'd say the risks are fairly equal across the board.
If I were to rank them on my own criteria, I would probably put them at
1. Moorea (with or without a Bora Bora option). Totally beautiful and peaceful.
2. Mauritius. A bit edgier, much more crowded (off resort) with an Indian influence.
3. Fiji. It was okay - not in a great rush to get back, although the friendliest people of the bunch.
If you are looking to cut costs and snorkel on the house reef, then the order would be
1. St Regis Mauritius
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2. Moorea (Sofitel la Ora in my case) - the coral here was so so.
3. Sheraton Tokoriki Fiji - lots of plants and low visibility
None of these compare to what you can get in the Maldives.
You can dig through my trip reports via my signature link to find the SPG properties at each locations; just look at the index to find the counties and go from there.
Best of luck!