"Commercial pilot" means a pilot who holds a commercial certificate. It's commonly done as an add-on to a PP.
There's really no special school for that; just about any school or independent instructor can provide that training.
Here are the requirements:
Be at least 18 years of age
Hold a private pilot certificate
Be able to read, speak, write, and understand the English language
Accumulate and log a specified amount of training and experience; the following are part of the airplane single-engine land class rating requirements:
* If training under Part 61, at least 250 hours of piloting time including 20 hours of training with an instructor and 10 hours of solo flight, and other requirements including several "cross-country" flights, i.e. more than 50 nautical miles (93 km) from the departure airport (which include Day VFR and Night VFR 100nm between points, with a time of at least 2hrs; also one cross country which is done solo 250nm one way, 300nm total distance with landings at 3 airports) and both solo and instructor-accompanied night flights
* If training under Part 141, at least 190 hours of training time including 55 hours with an instructor and 10 hours of solo flight, and other requirements including several cross-country, solo, and night flights
Pass a 100-question aeronautical knowledge test
Pass an oral test and flight test administered by an FAA inspector, FAA-designated examiner, or authorized check instructor (Part 141 only) With a CP, one can legally fly "for compensation or hire". This means everything from test pilot to banner-tower, and everything in between.
You may notice that no instrument or instructor's rating is required to hold a CP and get paid to fly, just the PP and the commercial.
However, they cannot act as PIC on flights carrying pax or cargo on scheduled routes, regardless of what type of aircraft it is... that is the privilege of the Air Transport pilot, aka the "airline pilot."
Now, if you're talking about becoming an
airline pilot, that's a different matter.
To act as PIC on flights carrying pax or freight on scheduled routes (for compensation or hire), you need an Air Transport Pilot certificate, which itself requires the instrument rating and commercial rating as prerequisites.
It can also be done piecemeal, but it's usually done through a school, typically a Part 141 operation. this may or may not be part of a university program.
As to what route to take, it depends on your budget, etc. Newly-minted airline pilots can find themselves finishing up with education-loan debts comparable to those of newly-minted doctors, and moving into airline flying jobs (if they're lucky) that provide an income lower than many fast-food employees.
Then there's the additional training, for type ratings (your ATP will not be enough to let you transition to jets, or even from one jet to another, in many cases).
It can all get very expensive, and nearly impossible for those supporting themselves to pay for the training and have time for it while somehow earning a living. Most go into hock up to their eyeballs, and it can take decades to earn a big enough salary as an ATP to catch up with those loans (and the interest).
I second the advice to consider a university primarily to get a back-up degree; the flight training can usually be had cheaper if you shop around.
I can't tell you much more than that, but maybe your next google search should be "airline pilot forums" or "commercial pilot forums". These are an excellent source of detailed information from people who actually fly for a living.