Your window washer is the tool you use to apply your window cleaning solution to the window. The washer essentially does the "scrubbing" and "cleaning", where as the squeegee does the "drying". Both tools are of equal importance.
There is a wide selection of washer sleeves on the market these days, and all of them are good for different reasons. Microfibre sleeves utilise the cleaning power of microfibre technology to give you as much contact with the surface as possible. Sleeves with abrasive pads are useful for windows with stubborn or caked on impurities. (Note, abrasive sleeves should not be used on the new soft glass that has hit the market recently). Many sleeves have acrylic fibres for increased durability and a longer life.
With the exception of the Wagtail washers, you have the luxury of being able to mix and match sleeves and T-bars. Whilst we usually recommend that you stick to the one brand, if you already have, for example, an Ettore T-bar, you could purchase an Unger sleeve and it will still fit.