Actually, the only real diff between Sport and Private is 10 hours of Solo training. But the cash is key.
If you wanted to fly, say a Cessna 172, you'd need a private and instrument rating. That's because the Cessna is rated for Visual Flight Restrictions and Instrument Flight Restrictions.
Each category requires training and endorsements. Sport pilot limits you to a certain category of aircraft and VFR flight only. Cessna 150s fall into LSA (light sport) category aircraft, which are flown by Sport Pilots.
Word to the wise: Get a private. Then Instrument. Afterward you can fly pretty much anything with one engine. If you wanted to fly say a cessna 310 or Piper Seneca, then you're looking at a Multi Engine rating. It all depends on what you want to fly. In my line of work it's in my best interest to get all of the above and go Commercial.
Now as for what's involved (abridged ver.):
Sport: 40 Hours w/ CFI and 10 Hrs Solo. NO EXAM (about 5-7K otd)
Private: 40 hours w/ CFI and 20-25hrs Solo. FAA Exam. (about 10-15K otd depending on who you hire the plane from and which CFI you go with)
Instrument: More time w/ complex trainers (retract gear)/Solo time and another FAA Exam (Expensive)
Multi: Introduction to Multi Engine flight characteristics/More time/Solo time/ exam. (mortage the 'maro)
Commercial: Bend over.
In the end, it comes down to flight hours and exams. Gotta pay to rent the plane, pay the CFI, pay for fuel and also learn ground handling/traffic rules and the like. Also, get those study guides they advertise. They work if you want to bypass classroom type ground schools.
Also, if you want to be a pilot remember this above all else: AP Mechanics and Line crews are your friends. Don't screw with them. (I am one.