Welcome to the wide world of stamps!
I collect U.S. only, but that includes the periods when the U.S. had possessions such as Cuba, the Philippines and Hawaii (although most of that is simply before the U.S. took over).
One of the neat things about stamp collecting is that what to collect is entirely up to you. It can be as broad as you'd like, or as narrowly focused as a single stamp issue from one country.
Keep in mind that even if you select only one country, the limits are only what you set. I mentioned I only collect U.S., yet it's a very large collection. There are mint singles, plate blocks, First Day Covers and ephemera such as post office bulletins, essays and proofs. It doesn't stop there though...there's airmails, special delivery stamps, officials, postage due and revenues. Still not enough? Okay, then add postal stationary and postal cards to the list. While you're at it, don't forget revenues.
Then, if you really want to expand the collection to the point you can't possibly finish it, try adding precancels. To have a complete set of ALL precancels would require somewhere in the neighborhood of 1.2 - 1.5 million stamps (and that may be conservative).
As you can see, the possibilities are endless. What's most important, though, is that you collect what YOU like, not what someone else likes.
Check your local area and see if there's a stamp club anywhere near you. You could join that and get to talk to some of the members who will be happy to show you some of what they collect. It's also a great way to obtain items. I'm the President of our club and we hold a member's only auction once a month where members can put up items for other members to buy.
There's also the American Philatelic Society. This is the national organization and it's not just for U.S. collectors. If you'd like more information, feel free to contact me and I'll be happy to tell you all about it.
I've added a few items to pique your interest for U.S. stamps.
This first image is a card proof (their classified by the Scott catalog number with the suffix P4 added, making this Scott 65P4).

This is a nicely centered common stamp with a Wheel of Fortune cancel. There are many collectors who like fancy cancels, another area of interest...

This is Scott 300 with a better precancel.

Maybe commemorative stamps interest you. Here's a 2 cent example from the Panama Pacific Exposition in 1915.

I mentioned plate blocks. Here's a plate block from the one cent imperforate issue, Scott 481.

Another popular are is collecting First Day Covers. Here's one which has all the issues for the 1934 National Parks. The last stamp issued was the 10 cent, which was issued on the date this cover was created.

Finally, here's one of the United States Revenue stamps. This is a better one, Scott 102c (the "c" means it has perforations all around).

Again, welcome to the wide world of stamp collecting!