Hello Medes. Welcome to the world of stamps. Its a good hobby that will last the rest of your life. I wouldn't get hung up on terminology as the terms have different definitions depending on who you ask. In my opinion, the pictures you posted IS the start of a collection. Don't let anyone else tell you otherwise.
To me modern U.S. stamps started in the late 1930s, but like I said, its not really important.
The stamps you have shown is a good start. $15 isn't bad, but you might be able to get a little more for your money by browsing
ebay or other stamp related sites. It's also a good place to get you a cheap Scott Catalog. Ones that are a few years old go for almost nothing. This will allow you to organize your collection. Good Luck