I would agree with the sentiment that you want to be neutral at the surface with your tank at 500 psi. and with a normal lung volume. This is most easily achieved by weighting yourself to float with a full lung volume and then sink slightly when you exhale.
Traditionally, divers weighted themselves with all their gear to float at eye level with full lungs and a near empty tank. This was in the pre-BC era where getting your weight right was important as any suit compression was going to have to be compensated for by the diver swimming the extra weight up and over weighting just made things worse.
The "weight yourself to be neutral at 15 ft" thing is not really correct for scuba divers. Freedivers on the other hand will weight themselves in this manner as it 1) allows a small degree of bouyancy on the surface to enable the diver to rest between dives, 2) does not present a large impediment to descending the first 15 ft and presents no impediment to descent below 15 ft., 3) minimizes the degree to which the diver is overweighted at depth and, 4) imcreases the likelyhood that the diver will float to the surface if they encounter a shallow water blackout and makes a rescue by the buddy easier.
None of this is really applicable for scuba diving as in scuba diving the ability to stay at the safety stop and them make a very slow ascent the last 15 ft is much more relevant. So it is much more preferrable to be neutral at the surface, not at 15 ft.
Prior to about 1980-85 when scuba started becoming big business and an every person sport, divers had to be very good swimmers and were all very comfortable in the water. Most also came from freediving (known as skindiving then) backgrounds and had bouyancy/weight issues nailed before they ever started scuba diving.
Today on the other hand it is common for rather weak swimmers with no freediving background to become divers. As an artifact of being less than fully comfortable in the water, many will be kicking or sculling with their arms even while trying to descend. This extra thrust is then offset by more weight and over weighting results from the effort to sink students with more weight rather than proper technique.
This is where people come up with the statement that your weight requirements decrease as your experience increases. It happens that way, but it shouldn't. The sad truth is that needing to be overweighted is indicitive of very poor technique and that the over weigthing itself in turn leads to additional bouyancy problems for the new diver. People should not even leave an OW class until they have become comfortable enough not to be unconsiously kicking on the surface when they want to descend.
Another related weight issue is the permanent compression that occurs in a realtively short time with a new wet suit. With a 7mm wet suit, this can result in the loss of a substantial amount of bouyancy. So while a new diver's bouyancy may be perfect with their new wet suit, several dives later they may be a few pounds to several pounds heavy and will again need to re-adjust their weight at the end of the dive with 500 psi in the tank.
It is always a good idea to check your bouyancy at the end of the dive now and then just to be sure nothing as changed.