Disclaimer: I'm not connected to these websites or brands even thought I use some of them. I'm offering links to good basic gear that you might find helpful. Feel free to do other research or purchase other brands, and by all means, if you can buy local, I hope you do!
Cymbals, pies, tins! There are endless kinds - hi-hats, rides, crashes, crash/rides, splash, Chinas, the list goes on. Figuring out where to start can be as tricky as buying a drum set. Different styles call for different varieties and weights of cymbals. A light washy ride cymbal used for low volumes jazz won't cut through a metal band. A mega bell heavy metal ride cymbal might be a bit harsh for a cocktail gig. But, if you only have one ride cymbal and you have to play both, is it the end of the world? No. Who knows, you might discover a cool new sound.
Listen to music you like. Try to pick out the sound of the cymbals. The bottom line is, do you like how a cymbal sounds? If this is your first set then don't get too caught up. Budget may be the determining factor at the beginning, limiting your options. That's cool! It was for me, too! The more you play, how you hear cymbals will change and you will discover the sounds you like and can seek them out.
I'm going to cover three kinds of cymbals, hi-hat, ride, and crash. You can investigate the others like Stewart Copeland, from The Police, playing splash cymbals, or Neil Peart, of Rush, playing Chinas later.
As you can see, the hi-hat is two cymbals stacked together. It's really just marching cymbals turned sideways and mounted to a stand. You can play them with a stick, use your foot to open close them, or both.
In most modern music the hi-hats are played as the main time keeper, a steady pulse that drives the music. In jazz, the ride cymbal is usually the main time keeper and the hi-hat is played with the foot on beats two and four.
Follow this link to look at and listen to some hi-hats made by Sabian. They are in order from least expensive to "people actually pay that much for hi-hats?" Yes, they do. Some of these have sounds bites so click through and give them a listen!
The ride cymbal is the other main time keeper after the hi-hat. It's played often in a jazz setting. In the rock and pop world, it is commonly used in the chorus of a song or during solo section. Rides are generally a larger cymbal with enough weight and mass so the sound can cut through the other instruments and be heard as a time keeping pulse. Ride cymbals vary widely in pitch and attack.
Check out this link to a bunch of ride cymbals made by Zildjian. These are in order from least to most expensive. Lots of other companies to explore as well. Many have links to sound bites where you can really hear the difference between cymbals. As with the hi-hats, you will also see a wide price range.
The cymbal next to the hi-hat on the left, pictured above, is a crash cymbal. Unlike the ride cymbal and hi-hat, the crash cymbal is used more for accents than time keeping. A fill down the toms with a crash cymbal accent at the end, lets everyone know you're now in a new section of the song. They help mark parts the tune(the verse, the solo section, etc). They can also be a time keeper for an effect. You don't get a clear attack with each strike, it creates more of wash over everything. It can be a great sound in the right place.
Like all cymbals, they come in a variety of sizes and weights. Jazz crashes are usually a bit lighter and rock crashes heavier to cut through guitar amps. If you are just starting out, medium and medium thin are a safe choice.
Here is a link to a variety of crash cymbals made by Meinl. Lots of different sizes and weights. Check out other brands and get a feel for the sounds.
Many starter drum sets come with a single cymbal and a pair of hi-hats. You can be guaranteed that quality won't be great, but you will have some thing to hit. If you want to upgrade the cymbals, you can buy individual cymbals, research above, or replace them with a cymbal pack.
If you buy a shell pack(drums only) you'll need to add hardware and cymbals. A cymbal pack is a great way to go. You'll get a pair of hi-hats, a ride cymbal, and at least one crash cymbal.
Here's a link a whole page of cymbal packs. Don't get overwhelmed but it's good to see that you have lots of options. Use the links above to research sounds then click through a couple pages and you should be in the ball park.
This is a lot to digest that's why I broke things down to a just three categories to begin with. You can check a bunch of stuff of just buy a pack that looks good and go for it. Either way, you get to start making music.
You made an interesting point when you mentioned that it is a good idea to pick out the sound you like when you are purchasing cymbals. My brother wants to purchase a drum set and wants to get a unique set of cymbals to go with it. It might be a good idea for my brother to do some online research so that he can learn more about how different cymbals sound. https://istanbulcymbals.com/