You can wash your bench, pipettes with RNase erase solution (commercial). Make an autoclave of you milliQ water, and use the filtered tips and tubes treated RNase free.
As above - you should use filter tips and RNAse free tubes, perhaps you should buy commercial RNAse free bottle of water, but for economy just use MiliQ. Clean your bench/pipettes with H2O2 3% solution if you don't have commercial RNAse eliminating detergents. It is also efficient.
Also, add to your reaction RNAse inhibitors and all will be fine.
DEPC-water is not for cleaning, it is for making solvents and using in reaction mixtures. Anyway, the advices are good. Use double-gloves, and change the upper ones sometimes.
If you want to clean your bench and make it RNase-free I recommend RNase away. This is a ready-to-use solution that can be used for surfaces, your gloves or pipettes or whatever. We purchase it from Carl Roth but I guess it is available from many other companies. You can purchase RNase-free tips and tubes from different companies as well but I know that these articles are very expensive. Normally it is enough to autoclave tubes and tips to make them RNase-free.
DEPC is just used to denaturate remaining proteins. After autoclaving this substance has no activity anymore.
All of the above plus everything that is heat stable -> 4 hours 160 - 200 °C all is sterile. I recommend it especially for all bottles etc for stock solutions.