Your Questions...

Q - What are the best types of houseplants?

A -  For ease-of-care, consider:

Peperomia - add a splash of colour with ivory and green variegated leaves - grows about 1 foot tall and wide.
Chinese Evergreen - can get to 3 feet tall in the right conditions - has attractive, bright leaves that thrive in lower lighting.
Dracaena - colourful yellow and green striped, strap-like leaves on upright stems. Good for open areas that need a tall plant.
Dieffenbachia - large green and ivory leaves provide a tropical look and will grow well in lower-lit areas.
Snake plant - tall sword-like succulet leaves are almost indestructible. It even likes dry soil between waterings. Grows to 4' tall.
Philodendron - an all time favourite - heart-shaped, trailing leaves add a touch of elegance  to any location.
Arrowhead Vine - another poplular houseplant, bright variegated leaves stay bright in low-light areas.

Q - What are some of the most common mistakes people make with houseplants?

A -
PIcking the wrong plant for the location it's going into - look at the lighting available where you plan to keep the plant vs. the plants lighting needs. Make sure they're compatible (same goes for the temperature).
Over/under watering. The soil should never completely dry out, nor should it always be soaking. Roughly the first inch of soil should be dry to the touch between waterings. Usually once a week is good, depending on the room temperature, location and size of the pot.
Not fertilizing. Plants do need some nutrition to grow strong and healthy. Use a time-released fertilizer that will provide ongoing nutrients for 3-4 months at a time. And always follow the label instructions to ensure you're not over-fertilizing.
Pot is too small. Once you start to see roots sprouting from the bottom, it's time to upgrade the pot so the plant can remain strong and healthy. Crowded roots will eventually suffocate the plant.