They work OK, but you save only a few dollars and they're sluggish in all operations. This saves money but can limit your ability to add fancier display capabilities later. A company named ATI makes some of the best of these chip-based circuits. Your eyes deserve to be treated well, so small monitors are a bad choice. Get one rated at 17 inches or larger.
Computers often come with modems as part of the package price, and most modems are adequate.
All of them will revert to a slower speed if lines are bad. Most are terrible. You might find one you like more. You don't need one to play games and run racing or aircraft simulators, but your kids will look at you funny for months if you don't get a joystick. Cheap ones are fine for beginners.