You should take a caddie your first time around The Old Course, unless you have had the chance to walk it the Sunday before you play. You will not always be able to tell where you are going otherwise.
Not all of the caddies are Tip Anderson, but every one of them knows more about the course than you do. Even if you draw the worst guy there, he can shoulder the bag while you are trying to figure out what the heck to do next.
This is absolutely spot-on advice from somebody who knows.
My first round there, shortly before Tom began his brief career as a St. Andrews caddy, was when I was a struggling starving student with no extra money for a caddy. My golf buddy and I were paired with a "disabled" North Sea oil worker who was a single digit player and who had a caddy. (That's right -- on a disability from Shell, a single-digit player, with money to afford a top-notch Old Course caddy.
He was a helluva nice guy, too.) Anyway, we made it clear on the first tee to the caddy that we were just a few years out of caddying ourselves, and it was our first time on TOC. The caddy was spectacularly nice to us, and we'd have been very, very much worse off without him. We threw a few quid his way in the end, and were HAPPY to do it!
You will have paid a lot of money to go to St. Andrews, and to play TOC. Not getting a caddy for your first tour around TOC is like giong to the French Riviera, renting a Ferrari, and then not buying any gasoline for it because gas prices are too high.