I’ve used pea gravel. In my area, pea gravel is sold in bags of mixed color round pebbles the size of, well, peas. It’s not foolproof for keeping the weeds down but it’s better than nothing. I’ve used sand, too.

Yes, the research I've done so far also suggested polymeric sand but some people suggested a silicone type of sealant application(?) I was wondering which will be more foolproof and long lasting?

You still haven't stated how wide the gaps are. Or shown a picture.

Polymeric sand is the routine method these days and it has many benefits. It's also relatively easy to use if you follow instructions on the bag. Some polymeric sand can even be used in gaps as big as 1/2".

A sealant would be a very unusual approach to filling paving gaps, though in a couple of specific instances I have used an elastic, acrylic caulk. Definitely not silicone.

If your gaps are big enough to receive gravel larger than chips then it's probably time to have your patio re-set.

We used polymetric sand and the gaps are quite large. Then we sealed the pavers. It lasts pretty good even with harsh Michigan winters. We do have to touch up every year after the first 2.

The biggest gap I see is 0.25"

There are a myriad of polymeric sand options. One consistent thing is that almost all the bags will state the widest gap for using that specific polymeric sand. We use sand by a company named Alliance. I'm not sure if their product is available nationally, but our results have been stellar. 0.25 is a good size gap but there are polymeric sand products that will work. Good luck.

neighbors have a large flagstone area - 30 by 50 at least and the flagstones were set in crushed granite that had been rolled.....after 3 years they are still fighting a battle with weeds "in the cracks" more than one landscaping company suggested this method instead of concrete does anyone have suggestions as to how to keep weeds down besides spraying with "roundup"?

Spray (or use a squirt bottle) the weeds with Vinegar. It will kill the weeds.