You will need the Olympus CLA-1 lens adaptor tube for your C-4000 in order to mount filters. Should cost about S$30 at CP or AP. This gives you a 43mm filter thread.
After that, you'll have to choose a filter size to standardise on and then get the necessary step-up ring and all the accessories you want (UV filter, polarising filter, ND filters, lens cap, lens hood etc). Many people like 49mm filters on the C-x0x0 series, but personally I went for 43mm filters with my C-2000Z in order to minimise viewfinder and on-camera flash blockage. The disadvantage of that choice is that it's awfully difficult to find 43mm filters in Singapore, but it's your call. Most importantly, though, just take time to explore and enjoy your new camera (especially after all the deliberation you went through in making your decision )