I have been using dirt cheap paint brushes (small ones, 1/2 inch + 1 inch) + vacuuming for years.
I had no idea there was such a thing as an "anti-static" brush for such purposes, but I suspect that such a thing is pretty pointless in reality.
My only suggestion would be to be careful whilst doing the cleaning job, such as don't move capacitors, don't touch anything you shouldn't with the bit of metal that clamps the bristles to the end of the brush, be careful with fans - they are much easier to damage than you realise and although it might be entertaining to make them spin at 10,000 rpm with a vacuum cleaner it buggers up the bearings as well as the motor.
As far as static is concerned all you have to do is be sensible, don't put on a fluffy woolen jumper and roll around on a carpet that is prone to static build up, don't touch the PCB with your fingers and so on, and I suggest turning off the PC, pull the mains cable and press the power button a few times as this will discharge the capacitors in the PSU and elsewhere.
I best add, I am a full time computer engineer, and I have brushed and vacuumed hundreds of motherboards, graphics cards, sound cards, network cards and stick of RAM over the years, I have never broken any of them, and I have never used an anti-static wrist band or any other anti-static device such as a mat - not that I am suggesting that you should do the same, I am merely stating that damaging PCB's whilst using a vacuum cleaner and brushing is far more challenging than many people believe, mostly because all PCB's made in recent years are coated with a lacquer that is there to stop static damage - NOTE: I am not stating that it is impossible, just that I have never caused any damage personally.
I have however broken or damaged some fans in my time, which is why I suggest using a great deal of caution.
One final point to make, static buildup and subsequent damage may vary a great deal where you are. Here in the UK we have carpets that don't create static easily unlike the ones made a few decades ago, and also static buildup happens much easier in low-humidity environments, the UK is generally not considered a low humidity place, and by sheer luck the brushes I have used over the years might have just been the right type to avoid static buildup and discharges - your mileage may vary.
A couple of suggestions about PC's and laptops that have been exposed to all of the vile chemicals caused by burning tobacco covered in additional evil chemicals added during a factory process, everything is sticky, dust and fluff sticks to the sticky smoke and simply put it builds up and clogs everything. I have often gad to remove the CPU heatink, remove the fan and soak the whole heatsink on boiling water with detergent to shift the orange/brown gunge and use a knife to carefully de-gunge each fan blade individually, you may even need to replace the fan as the bearing my be screwed up and it wont have helped that the fan has had additional weight added to it which wont have done the motor any good either. If you are going to remove the heatsink from the CPU, make sure that you don't damage the pins if you end up taking the heatsink off and the CPU comes out of the socket with it, and make sure you have some IPA and thermal paste to hand as you cant simply put the heatsink back on once it has been removed as the thermal paste dries hard over a few weeks/months.
NOTE: Compressed air in a can is very cold and can cause instant condensation and due to the cold can damage components because some may shrink and others may not although condensation is the main concern. Its ideal in very short bursts for small amounts of clean dust (not tar infested gunge) or for places that you cant get to with a brush, but be warned it can damage things.
Main PC, P180, CM Silent Pro 500M, i5 3570k @ 4.2Ghz, 8-GB @ 2,400MHz, 512GB 850 EVO, 500 Extreme II, 2x 2.5" drives, MSI 660Ti Twin Frozr.
Server, under reconstruction, 380W Enermax Pro82+, positive pressure only.