How do I swap weapons?

You can cycle through all of your weapons by tapping tab, or scrolling your mousewheel.

It is also possible to use the number buttons (1,2,3 etc.) to cycle through weapons. If for example, "1" is pistols, you can cycle through all of your pistols by tapping 1 multiple times.

There is one more way, the one I think is the best, to cycle through your weapons, and multiple ones in a category. You just hold down tab, and you get to see the entire weapon wheel. With the mouse you can select any of the weapon categories, and while still holding down tab you can scroll your mousewheel to cycle through guns in that category.

If you're playing singleplayer, the last one will also slow down the game. You'll have plenty of time to select your weapon. The other ones don't affect game speed.

If you buy a new weapon at ammu-nation, it will be added to your weapon wheel. There is no limit on weapons you can carry.