I have had goats for 30 years, and we always disbudd ours. The disbudding iron you are looking at is very affordable, but you have to wait between horns to let it heat up again. To be quite honest, it is a PIA!. If you are going to keep goats for more than just a little while, look up Caprine Supply on the computer. They have everything you could possibly need for raising and caring for goats. I highly recommend the Rheinhart (I think it is the biggest one they make, but I've had mine for 15 years now and still using it!) If you don't intend to have many goats for many years, your local 4-H agent or FFA agent could probably help put you in touch with someone to do it for you. A vet will probably want to cut them out surgically, which is very expensive and un-necessary if you have a 4-H or FFA.
You don't mention what kind of goats you have, and the horn buds in different breeds mature at different ages. HOWEVER! If you can feel them under the skin, THAT'S the time to burn them, BEFORE they erupt. You will get a nicer, smoother head on your adult goat, and more likely than not, you will not have scurs (partial growth of a horn that usually curls back into their head and has to be constantly cut back...a bloody endeavor).
Good luck!