Equipment Maintenance/Cleaning

Good advice given already, soft brush attachment, flexible hose, vacuum.
The paintbrush thing works well for a weekly (or so) brush off, but spend a few bucks and get a nice natural hair (horse, hog, etc.) brush, not nylon.
Dust with microfiber or cotton (not cloths containing nylon which can scratch). Consider a dusting spray that is alcohol and ammonia free and offers anti-static benefits - spray the cloth not the gear.
Get a dedicated plastic cleaner for plastic pieces. Novus makes a variety of products from a basic cleaner PC-10 to more heavy duty scratch removers.
Frequency of cleaning depends on where your gear is located (in the open, in a rack, in a cabinet) and also the ambient conditions and particularly how much air flow and dust are present in the area of your gear.
Here is one article on cleaning audio gear.
As to cleaning the insides, I have rarely seen the need (except in the cases of used vintage gear, electronics with fans, or my garage system) and I would think in most cases if cleaning the insides is needed then blowing the dust out with compressed air should do it. Personally, I would never own audio electronics with a fan, especially after cleaning out the fans on my computers over the years. Fans basically suck ambient dust into the gear.

Victrola HERE... YUP works perfect..

I have a pair of red center co axle drivers in Teak enclosures, pre WWI. Work perfect, 32 ohm speakers.. Silk surrounds, probably last another 100 years...

The 100+ year old solid Teak boxes are worth how much?

I agree with millercarbon about cleaning everything that carries a signal. I've been doing this every year forever. If I work straight through with no breaks it takes a couple of hours. Also, check the fasteners that hold the speaker drivers . If you can, use whatever tool the fasteners need to tighten them down. You may be surprised at how loose they've gotten. You'll hear the difference .   

Good point on the speaker driver screws to the baffle.  If you have one, use a torque screw driver or small torque wrench to get them all the same.  If you have access to the designer, maybe ask what torque to use or apply your torque device to one of the screws that seems to be reasonably "tight" and use the reading as your baseline for tightening the other screws.