Over the past several months, Jessica Burdeaux has come by the Reverb studio to help you build a drum kit piece by piece, depending on the types of music you play. If you haven't seen the previous releases yet, check out her videos for choosing the right snare and kick drum.
For jazz, Jessica suggests a lightweight, hand-hammered ride with semi-fine lathing and a traditional finish. This will give you a dry, articulate sound. That dryness will let quick sticking patterns be heard, while the other features will let it stand out in a mix of other loud, mid-range-heavy instruments like horns. The 21" Istanbul Agop Jazz Ride is a great option, but similar cymbals in slightly smaller or larger sizes will also sound great in small- or large-band settings.
For rock, you'll likely want a medium-to-heavy weight ride cymbal with a traditional finish, fine lathing, a strong bell, and pronounced taper. The heavier weight will project more through a mix of loud guitars, while the pronounced taper will let you use the cymbal as a kind of crash as well. Jessica's using a 24" Paiste 2002 Big Beat, but any similar medium-to-heavy ride will do the trick.
Finding a smaller-sized ride with an even more pronounced taper will be good for punk, because that size, fine lathing, and taper will allow for even greater crash-ability. Jessica's using a 23" Zildjian Sweet Ride, which is a favorite of Blink-182's Travis Barker, among other punk drummers.
If you're playing fusion jazz or, really, any genre that calls for complicated patterns, look for a ride cymbal that's a heavy weight and has a raw finish. This will give you a rich, dark sound, with a lot of quick decay—letting your intricate patterns be heard clearly. Jessica uses a 21" Zildjian K Custom Special Dry Ride, which will still give a strong ping without the harsh overtones you'd hear with other cymbals.
Finally, Jessica demonstrates the kind of ride that would be good for metal. A heavier cymbal with a strong bell and a brilliant finish will give you a pronounced, rich bell sound, so that your metronomic patterns are bold. The weight and finish make this less-than-ideal for crashes, but, presuming your metal kit has plenty of other crash options, a 21" Sabian AAX X-Plosion or a similar cymbal will work great as your ride.