Most of us have heard of different styles of rein handling, but we may not know that those styles have different applications.
As suggested, I believe the Achenbach style is appropriate and desirable for recreational driving with a well trained horse. It provides a relaxed position for holding the reins over a long period of time without tiring, yet provides for easy control. I especially like the ability to take up the reins in an emergency without running my elbows into the seat back or having to stand up and lean back.
Achenbach may be hard to visualize (without a mentor to guide you) but here a couple of links which provide both illustrations and descriptions.
I think the most complete description is provided by “ACHENBACH’S SAFE, SANE DRIVING GRIPS LEARN THEM IN THE COMFORT OF YOUR OWN BARN” BY KATHY HANSEN. This article includes illustrative photos and descriptions for the basic grips and dressage grips. The article is posted on Hans Out’s web site. (Note: This site is also an excellent source of carriage history.)
Coachman’s Delight Inc. discusses ‘Driving from the left hand‘ and the ‘Hungarian Position’ with nice colored illustrations and descriptions of the basic maneuvers. I’d suggest using this reference as a supplement to Kathy Hansen’s article. It may help clarify anything that is still uncertain/unclear in your mind.
Obviously the best way to learn would be from someone knowledgeable but we don’t always have that opportunity. As an alternative I suggest building yourself a rein board.
There have been many suggestions on what to use for weight on the rein board. Some suggest attaching weights, perhaps soda bottles, of about 1/2 pound each. Others like to attach a bit to better see the results of their practice. I suggest attaching small snaps to the weight end of the cords and using both weights and bits.
Using weights will give you a feel of what a 1/2 pound force (resistance) feels like and this is approximately the weight of the contact we should be striving for with our horses.
Using a bit may help visualize just what signal you movement is sending to the horse.
I really like the Achenbach style for leasure/recreational driving. It is an easy position to maintain for a long time, very relaxed. I like being able to take up the reins quickly without interference with the seat back or passenger. It keeps my whip hand relatively free for signaling without the risk of sending false messages via the bit. And when I anticipate a situation that may call for quicker rein aids I can quickly and easily switch to a two handed (bridged) position.