As a rule, you will want to get Selvedge jeans.... Raw denim is a purists favoriate, however they can be difficult to buy because they are hard to find and also they shrink. So, you have to be extra careful when choosing a pair because they will shrink duing the wash. It's best to go to a jeans boutique that sells raw denim and speak to the salesperson. They really aren't something you should buy online.
Selvedge jeans, on the other hand, don't shrink. They go through the sanforization process which shrinks them at the studio before they are put out for sale.
There are two types of denim that you are probably looking for: Raw or Selvedge.
Here's a good video going over the history of Selvedge denim, and its benefits.
Raw Denim is denim that has not been washed and doesn't go through sanforization.
Selvedge
Selevdge denimin can be hard to get, that's one reason it is to popular. It's also popular because it is a stronger weave. The denim will last longer, wear better, and looks nicer after a while. It is the original style of denim. If you're in NYC you could go to one of the boutique shops that import denim from Japan and have them tailored in New York, but these jeans might run you several hundred dollars...even close to a thousand dollars. The idea was parodied in the HBO show How To Make It In America.
However, you can get selvedge jeans without spending your entire paycheck. The best places are J. Crew and French Connection.
Here's the J.Crew selvedge jean.
This selvedge Jean is from French Connection.
Here's a selvedge jean from Ralph Lauren
Raw Denim
It can be super hard to find raw denim jeans online, mostly because there are so few stores that carry them. People tend to want jeans that won't shrink....and raw denim jeans will shrink. The one benefit to raw denim jeans is that they fade naturally. However, they are a lot of work. If you really want to get a pair, then here are some boutique brands that you can search for.