The strike plate is a rectangular metal piece that attaches to the door side, with a round or rectangular hole in the middle for the latch to slide through. If you are installing a new latch, you will likely need to remove the old strike plate. Most latches come with their own strike plates.
The latch plate sits on top of the latch and allows it to rest on the inside of your door without scratching it. Rectangular is standard for most door latches.
Do not buy any additional screws. If your latch needs screws, they will likely come as a set.
Most door knobs are affixed to the door with 2 screws on the top and bottom.
If your door is old and in need of a new paint coat, you may want to paint or refinish the entire door.