I'll run at odds to all the other answers, so far. As someone who spends the majority of his time on builds and fit-outs, I'd say the same as a lot of my colleagues, namely for fixing skirting boards, etc into position with screws you'll ideally want to sink the head of the screw under the surface then either pellet it or fill it. For that twist drills alone are far from the best of solution. Best tool I've found for the job are these Trend Snappy drill/countersink bits:
which will sink neat holes big enough to hide the screw head out of sight. The no. 12 size, which takes a standard 3.5mm twist drill, is ideal for 4, 4.5 and 5mm screws. There are other brands, but the Trend Snappy ones, whilst not the cheapest, have a major advantage - the firm sell matching tube plug cutters in 3/8in and 1/2in sizes to match the diameter of the counterbored holes produced by the drill/countersinks (the no.12 bit requires a 1/2in plug cutter).
All these tools can be used in a cordless drill, the replacement twist bits can be sourced from any supplier of HSS drill bits (try Toolstation - they sell or sold Milwaukee Thunderweb and/or Heller) and the lower cost steel bodied drill/countersinks can be resharpened using a file - as opposed to the much more fragile TCT Snappy bits
In point of fact most softwood skirting boards these days are fixed using either a grip adhesive, such as GripFill, or using a low-expansion PU foam, and 16 gauge nails are driven through the face of the skirtings to hold them in place whilst the glue sets.
The old technique was to cut wedges with a side axe which were then hammered into gaps chiselled out of mortar joints in the masonry to which the skirting was then nailed (with oval nails in more recent times) is seldom used these days except on listed building work (where we might well be using cut nails instead), although it does still have its' uses for tasks such as securing wooden window linings to masonry where there are no timber grounds to work onto