I have used a pouch I found on Amazon with great success. The specific bag I am using is the black version of
(Amazon/commercial link removed)
I hang this pouch on my left armrest. The zippers have pull cords on them I can hook a finger through which makes them easier to open. I would have great difficulty operating just a zipper pull, as I can't squeeze much between my thumb and fingers.
These pouches cost less than $20. Depending on how the wheelchair's armrest is configured, it might require some ingenuity to mount it.
On one of my wheelchairs I used a thin strip of aluminum plate with holes drilled for bolts that went into nuts instead into the unitracks on the bottom of a Permobil armrest. That worked great.
The pouch is easy enough for me to access and holds a surprising amount. I typically store a pair of warm gloves, sun gloves, hand warmers, sunscreen, and various other misc. items. There is plenty of room left over for a phone. When riding around in Yellowstone, there is even enough room for a can of bear spray.
I carry water bottles in the two water bottle pockets on the pack I hang on the back of my chair. That pack contains rain jacket and pants, warm hat, poncho, a complete toolset, pump, tire repair kit (I often ride pneumatic tires), spare tube, etc.
The pack I hang on the back is an Eddie Bauer Highpoint 30L. This pack is easy to hang on the back of a wheelchair and holds all the stuff I want in a convenient way. After looking at around 50 packs and experimenting with 4 different packs on the wheelchairs, this is the one I have settled on. These often seem to go on sale. I think the last one I bought was around $30 or $40 on sale. I did a quick check and they are currently $45 at Eddie Bauer's website (after 50% discount).
Four of my five wheelchairs are set up with these two items. I am very satisfied with them.
Steve