The "standard" practice is using a sharp center punch on the mark, then a small diameter drill for a starter hole, or even a pilot hole.
For more accurate marking when you are working on metal, paint the surface with an indelible marker, then mark the spot to be drilled by scribbing a cross on the painted surface with a steel point. This will make it much easier to see the exact spot where to punch.
Any twist drill will wander somewhat if you don't mark the spot with a center punch to start with; the smaller diameter ones wander because they tend to flex, the larger diameter ones wander because the web off the drill is too wide to start an accurate hole. A large diameter drill may need a starter hole even if a center punch was used. I usually drill starter/pilot holes for any hole over 3mm final diameter.
As I have a rather small and low-powered bench drill press, when drilling metal, after center punching I usually start with a 3mm drill (unless the hole is smaller than that, of course), then up from there in 2mm increments up to 0.5mm under the final size, then finish to the final diameter. This has the advantage of reducing the stress and wear on the drill press and giving a cleaner hole. Of course, the successive drillings must be in as perfect indexed to the spindle as possible so the hole stays true, and ideally the part to be drilled should be well clamped to the DP table.
The downside with this method is, if you go from a very small sized, short drill bit up to a rather longish one, and the spindle on your DP has a shortish stroke (mine is just 50mm) - say, starting with a 3mm drill and going up to 10mm, for example - you may have to adjust the position of the table to get enough heigh for the longer drill. This will need some very careful repositionning, so a good beforehand preparation is needed. But it can be done if you are careful enough.
Edit: almost forgot - when drilling hard metals use some form of lubrication, otherwise too much heat will be generated.