When you get your
clubs extended, also get the lie adjusted. Being 6'5", you will probably need to be adjusted about 2* up. Just lengthening your
clubs will not help you. Once you get all the adjustments made, you will not need extensions longer than 1 1/2 - 2". There is no worry about your club breaking or any damage. It is simply a piece that fits into the butt end of your golf club. What will happen though is with the club being a bit longer it will affect the flex of the shaft - the flex will be slightly softer.
If the extension breaks or comes loose it is simply beacause it was not installed correctly. The epoxy used to attach the extension to your shaft butt is the same as what holds your shaft tip onto the club head which is moving much faster and takes on WAY more torque than the top of your shaft.
Your price is going to be mainly based on the type of grip you choose. The extensions are inexpensive and easy to install. The re-gripping is the more expensive part of this process.
If you are willing to pay a bit more, you may just want to get your
clubs completely reshafted. This should cost you about $30 per club. This will relieve all worries about breakage and shaft flex - as long as the builder knows what he is doing. Again, if you are spending that kind of money, get the lie adjusted as well. There is no sense lengthening the
clubs without the correct lie.
As I mentioned above, being taller you will probably need the lie adjusted up about 2*. If you do not get this adjusted, you will be taking divits with the toe only of your
irons. This leads to thinned shots from the center. If you can only afford either length or lie, choose lie. Adjusting the lie makes the club more upright and will give you a bit more length.