Well, it all depends on what accuracy level you want ?
Deep hole drilling has some considerations that rise above normal considerations
Unfortunately, it conflicts with many of the "standards" we have learned in our machining careers or hobby. So let me begin :
Lathe work- First know that that your tailstock , may not perfectly match the C/L of your spindle OR the writer who mentions he has perfect accuracy ? And this measurement must include parallelism of the spindle and tail-stock quills !
Mill work- How much spindle run-out do you have , both in bearings and "tool" holder readings?
I am not being a jerk by mentioning the above , but trying to point out that no two people will achieve great results because the subject of Deep Hole Drilling (DHD) boarders on Art Form and success is based on approach and machine( + tool) capabilities !
Here are some pointers , at the Die shop I worked in , we did DHD every day and to 25 to 40 x diameter. So what are normal perimeters you ask ?
For gundrilled work in a gundrill lathe you can achieve .0001" per inch drift or less
For gundrilled work in a mill , you can achieve .0015" per inch drift or less
For conventional drilling without prep, it is not unusual to see .010 to .020" per inch drift
The difference you see is because having the "work" piece turning will always produce more accurate holes as the lathe's axis redirects the drill bit far more than the drill bits axis does.
So if you want straighter holes, use your lathe.
The single, and most important factor to a straight hole is ...."Hole Prep"!
Center-drills and Starting drills do not cut it !
Small drills or step drilling do not cut it ! ( more later here)
To start the hole, use a Ball Endmill or bore the hole -finished size... to a depth of 2 x diameter
Few machinists know or realize that a Ball Endmill is one of the most precisely ground tooling they have and the nature of the ball form drives that cutter to a precise round hole.
Then having a hole with 2 diameters depth, the "flutes" of your drill bit will be automatically fully supported ( 360 deg) to give you the best chance for a accurate hole.
Now if your lathe is under powered, you can still do your step drills, but first having the hole prep done properly, when you use the full size drill, your load will be less, but the drill will have support from the prep area and produce a much straighter hole .
For example, a 1/4" drill bit is much stouter than a 1/16" drill and having the 1/16' drill first means greater chance of deflection, and if you want the bigger drill to follow the same path, you cannot expect superior results.
The only problem with Ball Endmills is limited size availability ( by 1/8 or 1/16"), but even so, use them whenever possible for hole starts. I never use a center-drill, unless it is on a shaft for tailstock support . For regular drilling I use a starter drill in the mill. And if the hole is a normal hole when in the Lathe , I use my drill bit, (yes ! ) but that should be another posting for that technique is 100 years old and not taught anymore -but give dead center holes.
Rich