Failure vs. success rate - You can expect around a 70% success rate once you've gained some experience. This number can be significantly lower if you're just starting out, which is why I highly recommend that you get as much cheap wood as possible to do a couple test runs with your methods, rooting medium and frequency of watering. I also recommend that even if 1 cutting is an available option, you at least get a second. Even myself with a 75% take rate chooses to receive 2-3 cuttings whenever possible.
Size - The standard size you should expect is pencil thickness with at least 3 nodes. Because of the nature of what we're dealing with, that's not always possible. Sometimes cuttings are a little thicker, thinner or shorter than what you'd prefer. I can assure you that I've rooted cuttings that were all shapes and sizes, funny looking, the runts of the litter and were much thinner than a pencil. Looks can be deceiving and until you try, you'll never know. However, there's nothing wrong with having high expectations, but it is up to the buyer to be informed prior to purchase. If you want to know what state the cuttings are in, ask beforehand. From the seller's point of view, it's much more beneficial to them for you to ask beforehand instead of complaining after the fact. Sellers want happy customers and sometimes they don't have the time to post what the cuttings of each listing look like.
Thin vs. Thick cuttings - My personal preference is for thick cuttings, but only if I'm rooting. It's much more difficult to graft thicker wood, so it really depends on your objectives. I can tell you that thicker cuttings take a bit longer to put out roots than their thinner counterparts, but when they do, it's usually a much bigger explosion of growth on top and on bottom. Not only this, but thicker wood usually has more carbohydrates and moisture stored within. They're more difficult to rot and it's more difficult for them to dry out. This is why getting cuttings from in ground trees can be an advantage. The growth at the end of the season will be much thicker. Having said all of this, there is a point at which a cutting is too thick and it becomes very difficult to root. Just make sure that you are receiving 1 year old wood and it's roughly no more than 2 inches in diameter.
Lignification - A common misconception is that cuttings that are not fully lignified won't root as easily. This is false from my own experiences of rooting fig cuttings the last 6 years and I would actually argue the opposite. However, there's nothing I've read in scientific literature to support either claim. In fact, it's very easy to root non-dormant green unhardened growth taken during the summer assuming you have a good misting system. Another common misconception is that fully lignified cuttings will last longer in the fridge. Again.. There's absolutely no evidence to support that claim either. What is a much more logical perspective is that the higher wood on the branches are usually not as lignified. The higher branches are also not as thick. The truth here lies in the thickness. Thicker cuttings usually contain more carbohydrates and certainly contain more moisture within, so if the level of lignification is what you're blaming, it's very possible that the true reason behind your theory instead lies in the thickness of the cutting.
Cuttings freezing in the mail - It is of course possible, but it's very unlikely. Maybe someone reading at NASA can help us out here with the physics, but I'm pretty sure that it would take quite a bit for cuttings to freeze that are wrapped in a layer of plastic and then also wrapped in a bubble mailer. If the USPS facility the package is hanging out in overnight is a freezer, that certainly will not be a good thing. However, I can tell you that the duration of being inside said freezer is often a point frequently left out of the equation.
Proper storage - As I have discussed quite a bit, the proper storage of fig tree cuttings is critical. What you're trying to avoid is the cuttings drying out or the cuttings being in an environment that is anaerobic. Just like in nature when organic materials are too wet and don't have enough air flow, that's a recipe for rot. You don't want to replicate that in your fridge, which is why I personally think it's best to wrap your fig cuttings in 2 layers of plastic. This allows some air exchange, it traps moisture so things don't dry out, but also you're not contributing to moisture by adding things like moist paper towels or sphagnum peat moss. Mine are wrapped in bread bags and then placed into a zip lock bag that is not zipped shut. In this state, I've had cuttings last longer than a year in the crisper drawer in the fridge.
Problems to look for - It's not uncommon to receive cuttings that may have been stored improperly. Even if they were freshly cut, if they were sent in something that's very wet, dry or doesn't have good air exchange, that's where things become justified in the recipients' favor. What you're looking for is signs of rot (the bark is easily rubbed off), black decay on the cuttings, white mold (this occurs quite frequent on leaf scars that were left on the cutting. Just remove the leaf scar. Problem solved.) or wood that is shriveled to the point that the cambium underneath the bark is no longer green. Sometimes wood still on the tree can have a shriveled appearance and can give the illusion that it's dried out. This is far from the truth and could be a sign of further lignification of the branches. Be sure to check the cambium for signs of issues. As always wash the cuttings on arrival, lightly brush them or use your hand to remove surface issues, overwintering pests, leaf scars and breba figs.