We imagine the bed of a river as a road on which water flows. It is not so. Especially in rivers subject to level variations, stones, branches, trees roll, get stuck, pile up on the river bed; but also sheet metal, iron, glass, ropes. The bed of a river with flowing water is one of the most dangerous places to walk: danger of injury, snagging, death. As a general rule you shouldn't walk in the river: you should swim. However we must protect our feet well for the inevitable contacts with the ground, in and out of the water: moreover, entering and leaving the river can take place in very inconvenient places.
As shoes, if you don't wish to spend 100 euro for proper river shoes, I recommend light walking boots (for example in Italy we can buy such shoes with some 20 euro at Decathlon). Size should be +1/+2.
On the feet we can wear synthetic socks or, if it's cold, 2-3-5mm neoprene socks.
The river helmet has multiple functions.
It is a protection in case of a fall.
It is a protection against impacts above the river (e.g. branches).
It is a protection against underwater shocks (e.g. rocks).
It is a protection from the cold.
The helmet for our uses must be a helmet for water sports: it is a relatively light helmet, it has many openings on the shell for water drainage, it has closed cell padding which does not get soaked in water. It can be with/without ear flaps and with/without the chin guard: there are advantages and disadvantages for each conformation.
I use a helmet with ear flaps, no chin guard, and I usually wear a simple cap with a visor under my helmet.
They protect knees and shins from impacts that can occur on the board or in the water against rocks and logs. They also protect the wetsuit from tearing.
They must be of the right size and well worn.
They can be found second hand used for the sport of downhill, in Italy for around 30 euro.
The river sup paddle has a fundamental difference with the sup paddle in open water: it has no angle between the shaft and the blade.
In all types of waters, but especially for river sup, I am against adjustable and divisible paddles.
For river sup I use a paddle length of about 25-30cm more than my height. But most river sup experts prefer a length about 10cm more. The length of the paddle is much a personal matter.
For long touring I use a carbon Mergner, made by a German artisan.
Most of the time I use this policarbonate blade Ainsworth, which I ordered in special configuration with aluminum shaft and this T-grip, which I prefer in order to hook the handle of a sup or a tree branch.
I use river paddles about 25-30cm higher than me.