The thing to remember is to suck up all the dust first, thats the most important part. No special vacuum cleaner is needed but the bags and filters will clod quickly so have plenty avaliable. You dont want the cleaner to be blowing dust back out again. Dust mop sweeping -dry or damp- is only suiteable for picking up light to medium levels of dust. It can be one of the most effective ways of cleaning a large smooth floor surface but it is limited to being used on what you would call 'clean' floors. It will clog fast. You can do it your way if thats what you think is best and its what you had quoted for, but remember in cleaning there are no short cuts. You reap what you sow and unless that floor is spotlessly clean before you buff it you will be at it all day, with poor results.