If you are doing full boils for 5 gallon batches, some sort of dedicated burner is necessary. In order to end up with 5 gallons of beer in a full boil, you need to boil around 6 to 6.5 gallons of wort. Most home stoves just can't do that. In order to do full boils you will need at least a 30qt pot, so yes, keep the pot that came with it.
Full boils are usually considered better since you aren't boiling a concentrated wort like you do when you top off after the boil. A less concentrated wort will develop less kettle caramelization and melanoidin formation, which can help making lighter colored beers.