If they really are that battered then id suggest you hit it with Prochem Power Burst then bonnet mop over the top, This will give you the best of both worlds plus will help dry off the carpet tiles. If they are not that bad then you should get away with bonneting, Fusion by Solutions seems quite good on tiles. Regarding which type of bonnets are best id suggest Charly pads which can be purchased from Alltec, if you dont do alot of bonneting then this may be expensive so it may be worth getting the Prochem cotton pads. Micro fibre pads are not much good so i wouldnt go for them.
Richie.