Depends how dirty you want to get 
I've used and discarded loads of miracle junk over the years, this is where I ended up...
General light dust removal off the disk - I use a carbon fibre brush. Dead common, get one from Maplins or eBay. I found mine shed some fibres at first, but now that it's broken in it works faultlessly. A Watts dustbug comes a close second, but if your Beogram has a low profile lid then you'll have to custom make a pivot for it.
General light removal of fluff off the stylus - I use the little brush that came with my Soundsmith cartridge. Looks like its carbon fibre too. Watts made a stylus cleaner, works great but can leave a fibre or two caught on the cantilever stem. (Google Cecil Watts and you run down a pdf of a pamphlet he wrote on the care and cleaning of records and styli.) Avoid those miniature toothbrush things that are included with record cleaning pads - too harsh.
Embedded fine dust removal, for those disks that haven't been played for 20 years - I use a Knosti washer, using distilled water with a few drops of photographic wetting agent. Wash again with pure distilled water to rinse, and leave to drip dry.
Encrusted muck removal off stylus, if you have played a record that has been anti static "treated" - same stylus brush again, but dampened (NOT wetted!) with distilled water. And patience.
Horror story serious muck removal off the disk, for those Oxfam bargains - the Knosti again, using the cleaning fluid that came with it. Contrary to the blurb it does leave a deposit (according to my stylus) so follow up with a distilled water rinsing.
Worse than that? Be careful, a frisbeed LP can be dangerous if it hits someone! 
Cheers, Steve