Root canals done correctly have a 95% success rate at five years. Failures occur when canals are not discovered or cleaned/filled, or later because of fracture (vertical fracture of the root, or of the part of the tooth above the gums) often times because a crown is not completed in a timely fashion.
Root canal, foundation and crown depending on where you live should be around low-mid $2k. Extraction and placing a bridge (crowns on teeth in either side of the newly empty space) will be mid-upper $3k. Removing the infected tooth and having an implant (titanium) placed, with a foundation and crown will start upwards of mid $4k.
Implants never decay again, as they are titanium, gold, zirconia and/or gold, but can be subject to a type of bone loss similar to gum disease. Your "permanent" crown or bridge is not ever truly permanent. It is subject to tooth decay once again getting into the tooth at the crown/tooth junction, and of course is still subject to periodontal (gum disease) issues as before.
Removing your tooth solves one problem (active infection, once healed) but creates a new problem: How are you going to eat your nachos?? Some teeth are more strategic than others. Losing a wisdom tooth when you have two good molars and two good premolars means very little in loss of function. Lose a first molar when you are already missing a second molar, and you are seriously short of chewing power.
One last thought: simply taking antibiotics for a true pupal (nerve) dead tooth is only a stopgap measure. Definitive treatment (root canal or extraction) must be done soon to prevent an even bigger problem.....up to and including hopitilization/death from a bad infection gone amok.