Herring-gutted is when the line of the horse's belly goes diagonally upwards instead of more horizontal. Most racehorses are at least somewhat herring-gutted simply because they are SO fit. The trick is to get an OTTB that is relatively close to the norm for a normal horse, so that it is more likely to become a normal horse once it has had time to let down. The 7yo chestnut is the most severely affected of these horses, but they are all herring-gutted to some degree. HOWEVER, being racehorses in work, most of them will be normal given time to let down. The concern is that if you get a horse like the 7yo, it may not ever properly "let down" and a herring gut affects the horse's stamina, reducing heart and lung room. Depending on what you do, it may or may not be a big deal. For me, as a showjumper and eventer, I won't have a herring-gutted horse, but for horses that generally aren't worked hard (show horses, many pleasure horses), it is an acceptable fault.
The trick is to research the faults and their effects, and choose which faults you will accept. If you want a horse for hunters or jumpers, upright shoulders and pasterns will be something you can't overlook, as they will limit scope and the horse will jump with less-than-ideal form. They also affect movement on the flat, restricting forward reach and therefore forward movement - not ideal for dressage - AND they affect stamina.
A weak hindquarter is prone to unsoundness and limits scope and form over fences.
I think that the absolute standout in this field is the 6yo liver chestnut. That is a horse that will do well in show-horse classes, possibly moves quite nicely (conformation appears to allow it), and may well have a very nice jump.