Regarding modes, a good one to try is P. I have a friend who uses P mode exclusively. In this mode the camera sets the exposure somewhere mid range. You can then either change the aperture or shutter speed and it will change the other to maintain exposure. You can use this to get your head round the correlation between shutter speed, aperture and iso. Have a play
Regarding filters, the slim hoya is perfectly adequate
you can get one for less than £20. Hoya also do a triple pack containing a polarizer, a UV and an ND. Lots of people have a UV on their lens all the time. It doesn't do anything other than protect your lens. Some people believe it degrades the picture, others don't. I am not a sufficiently good photographer for my parameters to be noticably affected so I keep one on and only take it off when I am using another filter. The third is the ND. This is like sunglasses for your lens. If you are shooting in really bright conditions and you want to slow down your shutter speed to get the effect you want you need one of these