Bike doesn't brake immediately and comes to a squeaking stop. Do I need to get new brake pads?
You may need to replace the brake pads, and the brake calipers and levers are very probably out of proper adjustment.

As this is a safety issue, you should definitely have the brakes examined and adjusted by a bicycle repair mechanic. 

If you feel confident about making adjustments yourself, and have the necessary tools, there are a number of good resources that will show you how to accomplish the task properly. My favorite is the Park Tool Company YouTube Channel. They have a specific set of videos that deal with rim brake adjustment, including identifying the brake caliper types with links to the appropriate adjustment video. 

If the pads are heavily worn, or have hardened due to age you should replace them - pads are reasonably cheap. If braking is still not strong enough after making adjustments then you could consider getting a set of more expensive higher performance pads.