Zoom lenses of up to 200mm or preferable 300mm (or larger) would be best. With a larger zoom you can be farther away from the action and still get shots that look like your in the middle of it.
Also a fast as lens as possible would be good. f/1.2 to f/1.7 helps get nice depth of field and fast stop action shots.

In regular are your referring to 35mm lenses? If yes than "Yes"...some 35mm lenses are usable on new D-SLR camera bodies however there is a conversion factor if used on a non full frame camera.
This conversion can be 1.5x to 1.6x. As an example a 70mm standard lens becomes a 105mm (or slightly more) on a digital camera.

There are many kinds of filters for lenses. The two most common are:

UV Filter- Used mostly for protection of the glass from elements. It is a good idea to get one for each of your lenses and leave them on all the time.

Circular Polarizer- A special filter that rotates and changes the polarity of the light as it enters the lens. This helps filter and align the light waves making the colors POP and brighten. Used correctly it can also remove glare and reflections off glass and water. This filter does not need to be on the lens at all times.

All lenses have different size filters. Check on the inner edge for a ## with a circle and a / through it. This is the filter size. Common sizes are 52, 55, 58 and 62.

The Sony Cybershot DSC-f707 uses the original Sony Memory Stick...not Duo or Pro.
This memory can be a little tricky to find and the size will probably be small verses cost of memory.
This might be a good time to consider upgrading to a newer camera.