Most commonly the mistake that is made is that a triathlete will use a surfing wetsuit for their triathlon wetsuit.
This is a mistake, because they are designed for different purposes.
Specifically the shoulders and going to be an issue when trying to compete in an triathlon with a surfing wetsuit.
A triathlon wetsuit is made of neoprene, and is usually around a millimeter thick, which provides precisely the right specifications for a triathlete.
They are engineered to provide buoyancy to the triathlete, whereas this is less of a consideration for the surfer.
Remember the surfer is not really supposed to be swimming, they are supposed to be surfing, whereas the triathlete hopefully should not be surfing (a joke, of course).
Two keys would be mobility, and tightness.
Mobility is going to be a consideration for the triathlete, because you need to be able to perform athletically with the suit, and the triathlon suits are designed for specifically that purpose.
It should also be super tight.
Unless your breathing is constricted by the suit itself, do not consider going up a size.
The armpit and groin areas are the places to measure this.
If you have too much air in these areas, you will be more prone to chafing (although usually a little of this is unavoidable) and those air pockets will fill with water once you are actually swimming.
This will cause drag and add seconds or even minute to your time depending on your level of skill with triathlons.
A quick word about brands...
There are as many different manufacturers as there are body types, and each manufacturer has different lines for men, women, etc.
The best way to go here is to find one that has a type of suit that is made for your body type (especially for women) and to deal with a reputable manufacturer, as well as making sure that you get your triathlon wetsuit from a source that you trust.