Cessna 150
A Cessna 150 is a two-seat aircraft that generally comes with a Continental O-200-A engine that delivers 100 horsepower. That's not a lot of power, but at or near sea level, it will give you sufficient power to learn how to fly easily for a much lower cost than many other trainers.

Cessna 172
A Cessna 172 is a four-seat aircraft that generally comes with a Continental O-300-A engine that delivers 180 horsepower. Many trainer models used at higher altitudes - at airports over 4000 - 5000 feet above sea level - have the two rear seats removed to allow more versatility during training. Some clubs have 172s with an extra bonus: a 210-horsepower engine you can train in to get your high-performance rating.
Piper Arrow
A Piper Arrow, often known as a Cherokee, is usually a four-seat aircraft that comes with variations of engines that range from 140 to 300 horsepower. Some variations have six seats from the factory. Most trainer models come with the lower-horsepower engines, and many at higher altitudes - at airports over 4000 - 5000 feet above sea level - also have the rear seats removed to allow more versatility during training.
Piper Cub
A Piper Cub, is a tandem-seat tail-dragger that works best as a trainer near sea level. Its best attributes are its simplicity and affordability. If you can find a flight school that can teach you with a Cub, chances are you'll enjoy it thoroughly, despite the extra complexity of learning in a tail-dragger.

Firefly
A Firefly is one of the planes used by the UK Defence Elemetary Flying Training School, used for training army and navy pilots. They can also be found in flying schools across Europe, and for sale to private individuals, usually for much less than 50,000 Euros. You may find you enjoy learning in one of these.

Sunflier
A Sunflier is a new all-electric trainer aircraft manufactured in Denver that may be paving the way to the future of not just trainers. The Aero Electric Aircraft Corporation has designed it for three hours of endurance and a 30-minute recharge time. FAA certification is expected before 2020.

Sporty Aircraft
Many different styles and types of sporty aircraft are available, depending on the flight school you choose. Their most common attribute is that most are two-seat airplanes with low wings, generally with lower-powered engines than a Cessna 172, designed to get you your pilot's certificate easily at low cost.