To answer your last question first, YES. It is a good hobby of you are interested in history, geography, or culture. Many world wide stamp albums once had biographical info about each country. If you bothered to learn about these countries as you mounted the stamps, you gained knowledge. Then you had the option to study the design of the stamp and learn about the country and its people.
I wouldn't worry about counterfeit stamps until you start collecting expensive stamps. It doesn't pay to fake a cheap stamp.
You could continue to old collection or branch out in a new collection. Many countries have issued thousands of stamps (literally). You could try to complete your favorite country or go for a stamp from every country. Many younger collectors now collect 'topicals" which are stamps about a particular subject. It could be anything from thew 1960 Olympics to butterflies to coins on stamps..
I suggest you try to join a stamp club. This could be a terrific source of very inexpensive stamps. Purchasing from a stamp dealer could become very expensive and you might never get your money back when it comes time to sell.
Educate yourself about the hobby. Read some books on collecting, then go out and have fun!