Some very good points all around. Weasil's last comments regard through the fence operations, and almost all airports have ordinancs or policies regarding through the fence operations. These are often not very visible ordinances, but they can still bite you. Where these usually become a problem is when other instructors feel that you're taking business from them, and they report you or prosecute.
Finding work as an independent instructor is very difficult any more; few places will permit it, and many insurance policies won't touch it. Most still want a cut for use of their facilities, which as others noted, puts you into a grey area regarding who is really contracting and who is under an agreement of employment.
One of my jobs involves contract flying; I fly for a government agency in a civillian aircraft, and am paid by the civiliian operator, not the government. I am not an employee of that operator, however. I am recognized as an independent contractor. The operator is hired to provide the services, and I am subcontracted to fly the airplane. Taxes are not taken out of my pay, and no workers comp or other arrangements are made for me. It's all my responsibility.
The same may be applied to independ instructing, even if the money is paid to the flying club. Merely because the student doesn't pay you directly, doesn't make you an employee of the flying club or FBO.
The biggest concern for you should be your own liability, and coverage in the event of a mishap. If you're independently instructing, then you're independently liable and responsible for both your actions, those of the student, and the aircraft. Conversely, if you're in the employ of a club or FBO, then the FBO absorbs a great deal of that liability. You're still the first line of responsibility in your duty to provide proper instruction and a safe environment, but most of the time the FBO has the bigger pockets and you are therefore somewhat shielded.
All that goes away if you're instructing independently. The same for future liability. When yours is the last signature in the student's book and two years later the student balls the airplane up, they'll come back looking for you. I've experienced that first hand, nothing I did personally, but I had made a short check-out flight with a student (from the same airport where you're flying, incidentally), and years later the student crashed sans current flight review and current medical. Mine was the last signature in his book, and the masses came knocking for their cut.
I won out...but I hadn't been acting independently at the time, or entirely so. Had I been, I'd have had a heck of a losing fight.
If your'e instructing indendently, then providing the insurance you'll need may be a lot more expensive than becoming a rider on someone else's policy. In other words, you'll be a lot more insurable and protected if you're part of a group of pilots seeking insurance...than just you.
What counsel did your friend give you rearding independent instruction?
I'm a little concerned, personally, by your reference to time building. I hate that expression, passionately. If you want to build time, then falsify it. Write it in your logbook and go get hired somewhere. Lie. Do it fraudulently. That's all time building is worth.
If instead you're going to build flight experience by learning, aiding the student, and devouring your work, you'll find it's invalueable time in your logbook and in your memory. Timebuilding is cheating yourself and cheating your student or employer. Experience building is another matter completely. Build experience, not time.
You may fly the same hour and it may be either an hour of time to be logged, or a wealth of experience. The difference is up to you. Build experience.