Given my experiences as a firearms instructor, I would say that newbies should almost invariably be taught thumb-over-thumb. Straight-thumbs is very much a technique for the serious, dedicated shooter in search of maximum performance.

The most successful practical-pistol shooter in history (and still going strong after 25 years), Rob Leatham is one of the fathers of the straight-thumbs technique.

STRAIGHT-THUMBS
The straight-thumbs method of gripping a handgun, which today has become the accepted wisdom among serious shooters, was developed in the early 1980s by Rob Leatham and Brian Enos. I've always wondered how that happened. Of all the possible ways you could grip a handgun, why did they come up with that one? This article provided me the opportunity to ask Brian Enos exactly that.

He responded, "Back in the late 1970s and early 1980s in IPSC competition, there were certain accepted ways to do things: the Weaver stance, for one. And the way we gripped the gun was what a lot of people call the Gunsite technique, where you've got your right thumb on top of the safety, and your left thumb comes up over that. Also back then, it was considered very smart to curl your left index finger around the front of the triggerguard. That's what Kirk Kirkham taught me. When Robbie and I first started shooting, Kirk was the best. He'd just won the Nationals. He was, like, local hot dog made famous. I asked him, 'How do you do this?' He told me, 'Finger around the triggerguard, Weaver, push/pull, this/that.' I shot that way for a while.

"Back then, Robbie shot from what today we'd call a Chapman stance. He was just very natural, didn't listen to anyone, didn't ask anyone. I think our first big departure from tradition was [when], one day [when] we were practicing, Robbie just decided, 'I'm going to stop shooting with my finger on the triggerguard. I'm just gonna do that.' By the end of the day we were shooting at 50 yards; Robbie said he felt like he'd never shot that good at distance. He wasn't that accurate of a shooter then. But he was doing really well and totally blaming it on his new grip: 'My new grip has done this for me.' So within a day or two I took my finger off the triggerguard, too.

"[When] the idea of pointing your thumbs straight at the target instead of curling one over the other came about, I was at the Steel Challenge. The first day, I had a horrible day, just one of those experiences when you feel like you've never held a gun before; the sights are kicking all over the place; it just feels totally foreign.

"That night in my hotel room, I started experimenting with changing my grip, just hour after hour of drawing into different grips. I'd noticed, when gripping the gun just with my fingers and palms, that that felt like a good, neutral grip, but when I added my thumbs, I felt like that extra pressure was causing the gun to track inconsistently. I wanted a technique that would take my thumbs out of my grip and off the sides of the gun so I was just gripping the gun with my palms and fingers.

"I started experimenting with my right-hand grip by only pulling front to rear with my fingers and just letting my right thumb rest on top of the thumb safety with no downward pressure. Then I noticed how resting my right thumb on top of the thumb safety opened up the entire side of the left grip panel, and I wondered, 'What if I just put my left hand there?' I rotated my wrist forward and pointed my thumb straight ahead, and that got my left thumb off the side of the gun. With the support hand I just squeezed left to right. So I wound up with front-to-rear pressure with the right hand and side-to-side pressure with the left hand, and that gave me very consistent, even pressure all the way around the gun.