Whether you get a root canal and a crown depends on if the tooth is restorable or not. That depends on several factors which are specific to your tooth and the surrounding tissues. First off, consider the following:

1) natural tooth is in many cases superior to fake teeth (bridges, dentures, etc.)

2) implants make a great replacement of a single tooth instead of a bridge

If the tooth has a lot of root structure left and can be easily saved with a root canal and a crown, go with that. If your dentist is skeptical that you will get much use out of the tooth if it is restored this way (i.e. it has a poor long term prognosis) then consider not doing this. The reason is: you could dump a few thousand dollars into the tooth and it would only last you a few years. You need to ask your dentist what are the circumstances that would make this tooth have a good or poor long-term prognosis.

If the tooth should be extracted, you should consider a single tooth implant versus a bridge. If the adjacent teeth are unrestored, you are doing more harm in cutting them to support a bridge than you are in doing good to replace the missing tooth. This is why an implant is a great treatment option. If, on the other hand, the adjacent teeth are in need of crowns, you can do a bridge and restore those teeth as well as replace the missing tooth with one restoration - sort of like hitting three birds with one stone ...

Implants are a great restoration. A properly placed implant can last indefinitely; in fact, the 10 year survival rate for implants is over 90 percent! It will be most like a tooth. Bridges can be hard to keep clean with brushing and flossing. This predisposes the teeth that support them to further decay and breakdown. An implant does not get recurrent decay; it is more like a tooth in terms of flossing and brushing.

Implants can be about the same price as a three unit bridge depending on the circumstances. If you go to a dental school to have the work done it can be significantly less expensive than having it done in private practice (as little as half or less than half the price).

The least expensive route would probably be to get a root canal on the tooth and then crown the tooth. The implant, depending on the circumstances (there may be other procedures necessary to prepare the bone to hold the implant) may be less, as much, or a bit more than a bridge, but will be more expensive than the root canal and crown. The bridge can also have hidden costs. For example, if the teeth that are going to support the bridge are not in a good position in the bone, they may require root canals, or if they have decay they may need root canals ... etc etc. So, a bridge isn't necessarily the cheapest option. Again, a good approach would be to do a bridge if the adjacent teeth need fixing anyway ...

As for time, implants will take the longest to restore (several months) because the implant needs to heal into the bone. Some practitioners and patients will try to rush this step which is never a good idea since it ultimately determines the success of the implant. A bridge will take less time to finish than an implant. Restoring the tooth with a root canal and crown will take the least time (just a few visits).

If your dentist doesn't want to talk about all three treatment options, the costs involved, the procedures involved, the time involved and the long-term goals of each treatment option, get a second opinion.