The largest problem you will face when measuring small Hall signals is the geometric error of the Hall element itself. A typical Hall coefficient of a commercial Si Hall element is on the order of 200 ohm/tesla. This is plenty for measuring fields on the order of 10 µT! However, the zero-field offset can be several Ohm typically.
Let's say you get one with 1 ohm offset. If you read this element at zero field, you read 1 ohm Hall resistance and could infer a (erroneous) magnetic field of 1/200 Tesla = 5 mT -- or 100x the Earth magnetic field. So you see how tremendous the typical offset is compared to the Earth field. Worse, this offset drifts with temperature.
Using AC-current as suggested by Neil does not remove this offset, as this is not a voltage offset, but an offset of the Hall resistance itself. Instead, you need a quadrature excitation which means changing the current axis through the Hall cross and averaging both measured Hall resistances. This is fairly complicated to do manually without digital processing.
Therefore, many companies offer Hall ICs that integrate a Si Hall cross and the switching circuitry to implement the quadrature excitation and a gain stage to output an easily readily voltage. One example is the DRV5053.
Finally, using metals as the Hall element itself is a rather poor choice. Their normal Hall coefficients are far smaller than Si. If you insist on it because of reasons (metals scale better to very small dimensions, metals are more ductile and exhibit less strain sensitivity) some metals like Bi indeed have appreciable Hall effects when made very thin. Another option for large Hall coefficients from metals is exploiting the anomalous Hall effect. In any case, using metals is probably off the chart for hobbyists because it requires special thin film deposition equipment to fabricate the Hall element.
