Compound microscopes are traditional microscopes. Usually each microscope has a few objectives which are rotateable. The common compound microscope have the objective powers of 4x, 10x, 40x and 100x. The other objectives are also used in many situations: 1x, 2x, 20x, 60x, 63x, and 80x. The eyepieces are usually of 10x, 16x and 20x.
The total magnification of a compound microscope has the range of 10x to 2000x. Most biological compound microscope has the light from the bottom so the specimen will need to be on a slide. It's transparent and the light will go through the specimen and enter the objective.
The other factors will affect to the quality, performance and price for a compound microscope are:
Stage: mechanical stage or manual clamps
Light: tungsten, halogen, or LED and the power of each type
Condenser: simple lens, brightfield with iris, darkfield
Viewing head: monocular, binocular and trinocular
Noise piece: forward, backward (reversed), triple (3), quadruple (4), quintuple (5)
Compound microscopes are not designed for low power specimens. If you want to see some details of coins, stamps, rocks, circuit boards, jem stones and similar things, you will need a stereo microscope.