If you discovered a new cell, what characteristics would you use to determine which kind of cell it is?
Presence of organelles
I'm assuming you're talking about eukaryotic cells versus prokaryotic cells. If you look in a microscope at the new cell, if it's a eukaryotic cell, you should see a nucleus, and various organelles. In a prokaryotic cell, you should see free-floating DNA or RNA and ribosomes.
Size is also a factor. Eukaryotic cells are much larger than prokaryotic cells.
One more characteristic is the presence of flagella on the exterior of the cell. Prokaryotic cells will have flagella on the outside of the cell like a tail, whereas eukaryotic cells have smaller cilia (like mini-tails) that surround the cell and control its movement.
To determine whether it is a plant versus animal cell: if the cell has a cell wall and a large central vacuole (filled with water) and the presence chloroplasts as well as mitochondrion, it's a plant cell. It should also have a fixed shape as opposed to the animal cell, which is more spherical and variable in shape.