Do you stop the turntable or let it spin while you run e record brush

I use the Brush in the Link.
It is the softest Brush I have come across that has a dedicated purpose for LP Cleaning.
It has been reserved for Brand New Vinyl and recently my Newly Cleaned Vinyl, that is slowly growing in numbers.
All my Vinyl Collection is being cleaned since the beginning of 2021, and this has been a purchase that has been good to incorporate into the post cleaning processes for vinyl care
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The ASB -1 Dust collection is extremely good, and work effectively without the need to apply a force, the free weight laying on the LP will remove any surface contaminant in not much more than two revolutions of the LP.
I leave the Puck Weight off when cleaning as when on the LP, it shields the light source across the LP from a local placed lamp that is set to direct a light onto the LP Surface.
The use of the lamp really aids with showing off the surface contamination that settles on the LP in a very short space of time.
The Brush is also the only brush I have used that when thoroughly removing contaminant does not cause slippage of the LP on the Platter, as there is no need to apply a down force to the Brush.

I certainly don't see this brush as being responsible for labouring the TT's motor.

It does command a Price above the commonly seen prices, but the effectiveness of the clean, the not producing slippage and the other properties it is claimed to contain, that are more difficult to comment on, make it an item I am happy to own. 
It fits perfectly into the equipment purchases made to carry out a regime of Vinyl Care and ensure the Source Medium is off a high standard when in use.  
     
https://www.yukimu-officialsite.com/asb-1

@skchun 

I guess I should wash most of my records.

Absolutely. Not the highest end cleaner, but effective, I bought a new Record Doctor V. Makes a big difference. Also have a basic Spin-Clean, which is great for dirtier records for a first clean.

I use a brush before every play, use a light touch. But, yes, I have found if my record drags while using a brush, that is a good sign it needs cleaned.

I use the Hunts Record Brush and sometimes the big brush with grounding I bought from MD. 

I never had good luck with record brushes, going back to the Decca. I’ve tried all kinds. They are good at pushing the dust into a line, but after that, advice typically is, push the collected surface lint/detritus to the label or to the edge, which is not, in my estimation, a good way to get rid of surface "lint." (Nor has "scooping" worked with the Hunt Brush, which I’ve had in various incarnations over the years).
I do a serious deep clean of a record (Monks: KL) and after that, use a third party inner to store (keeping the original if it has artifact value). A lot of the "audiophile" inners shed. After using a lot of different inner sleeves, I have settled on two--- the round bottom Japanese ones- sheer and not much substance, or the MA Records liner which is pricey and like a woven fabric (made from plants, I believe). The Japanese ones seem to leave the least amount of shedded material.
The issue for me is maintaining cleanliness. Whether that is exposure of the LP surface in unsleeving, playing (vortex action per Percy Wilson) or my skin shedding, I always find some surface lint on a record even after it has been deeply cleaned and properly sleeved. (I sleeve outside the jacket, using a outer jacket cover for this purpose). The room is dedicated, pet free, and rarely has any traffic apart from me.
I keep a hand held air puffer and a piece of silk handy for this surface clean up.
There is one brush I tried that I liked- it had some anti-static properties-- the Analog Relax-- but on balance, the problem isn’t really a strong static charge, just surface crap (which might be attracted because of some slight charge).
@Antinn got me to buy an anti-static cloth which I am going to try in lieu of the silk cloth.
You may have a different experience.
I look at the records under a pretty strong light at the turntable, am constantly dusting and vacuuming to keep the area clean, but it is the nature of the thing-- I’m not in a clean room wearing a special suit and goggles.

wash batches of lps OFF the turntable while listening to clean ones.

then, after clean, all I deal with is paper dust from inner sleeves, or airborne dust on the surface, not in the grooves. I have a large lint free cloth like a giant camera lens cleaner. I lay it lightly on the LP, turn the platter by hand, a simple lift of the dust, play. 

No more habitual anti-static dust brush, i.e. discwasher. no squirting fluid and being to impatient to wait for thorough dry.

have a peek at my system photos, around the 10th one shows my manual batch cleaner. 10 lp. the drying rack is the thing.

I scrub aggressively with a baby scalp brush (amazon, 3 pack), use the lid of a Chinese soup container to protect the paper label, and the bath is rinse only, distilled water. my mix, kit cleaner, add more alcohol, add a few drops of dishwasher anti-spotting i.e. jet-dry as a surfactant.