I'm a relative newb, too (only had my lathe for about 5 years), and I had to make a precision bushing for the first time just a week ago. It was for supporting a pulley with an oversize hole on an alternator with an undersized shaft. Considering that the alternator will be spinning at up to 15,000 RPM, I figured that the whole thing needed to be pretty precise if the pulley was to turn true. I cheated, a little - I started off with a nice piece of DOM tubing, although it was well undersized inside inside & oversize outside, but at least it already had a hole...
In the past, I've generally just used drill bits, chucked in a Jacobs chuck. This time, however, I decided to use the "El Cheapo" brand boring tool set that I bought cheap (under $40 for the 12 piece set), years ago. As it happens, the boring tool holder that came with my "El Cheapo" QCTP set wouldn't hold any of the boring tools (hole in the tool holder was waaay too big), I rigged it up in one of the regular (rectangular) tool holders, using a shim to hold it more or less centered in the holder, and cinched it down. I used some spray-can cutting oil, and went to town on it. Surprisingly (to me, anyway), it went perfectly. I went slowly as I got close to final measurement, finishing off the inside with a piece of 600-grit paper wrapped around a small drill bit. When I was done, it measured out to within .0005", both inside and outside, and was a perfect fit. Interestingly, as the alternator itself needed work (new diodes) I took it to a rebuilding shop, with the new bushing & pulley installed. The tech who looked at it initially was so impressed with the bushing, he called in the rest of the staff to see it! I didn't think it was anything to get excited about, but they sure thought it was cool. It IS nice to be appreciated!
My point is that even a set of cheap boring tools (they look like the ones in Makerofthings' post, above, 2nd photo) can be very useful. I do have an odd selection of reamers as well (sourced off Ebay, no rhyme or reason to the sizes), and use them often, but with my latest experience with the boring tools, I'm going to be using them a LOT more often from now on.