I am 20 years old, uninsured and I need a root canal on a molar. What are the pros and cons of a root canal vs. extraction?

Nothing compares to having your own natural teeth . Provided your tooth is restorable post- rct , which your dentist can assess, it is always advisable to save the tooth as opposed to having it removed. Replacing lost teeth may not always go according to plan and treatment might be complex. If possible, natural is best. 

If the tooth is pretty sound and you only need a root canal and crown, that would be the most conservative and least costly way of restoring your mouth.If the tooth is significantly weak, and not a good candidate for crown even after the root canal, then extraction may be the alternative treatment you might want to consider.It sounds like you are having financial issues, so be aware that an extraction and fixed bridge or extraction,implant,abutment and crown will both cost much more than the root canal and crown.Yes, of course you could have the tooth extracted and utilize a nesbitt partial until you're ready for the implant. It's your mouth, the choices are yours.  I advise following the recommendations of your dentist.  He is the best one to evaluate your problem and unique situation and best direct you in the best way to address your problems.By the way, don't hold your breath about dental insurance.  Even those who still have it are finding that their benefits are decreasing almost yearly.  Oftentimes they won't cover implant treatments or fixed bridges unless the tooth is extracted while on their dental plan. Another reason why trying to save the tooth with root canal and crown may be the best way for you.

There is nothing better than retaining your natural tooth.  In the long run its less expensive to have a root canal and ultimately, a crown.  Depending on the amount of tooth remaining, you may or may not need a post before the crown.  Have the root canal done, have a post placed (if needed) and have a filling placed.  You can then have the crown made at a later time when finances are less of an issue.  I am confident that your dentist would work out a comfortable payment plan with you. 

Short n sweet:  save the tooth if it is reasonably savable.  There are NO pro's to having savable, functional teeth removed.  Not even financial.  Sooner or later you will be looking at a bridge or implant, etc, and wishing that you had saved the tooth!