Any reasonably-sized expedition into the wilderness or underworld will almost certainly need at least some animals to ride, or to carry supplies.
The best solution is to keep a variety of riding beasts, and choose the best ones for the given expedition. But this is too expensive for most frequent travellers, and incompatible with the roving life. The adventurer is most likely to buy animals as needed and sell them later. This, of course, has the disadvantage that the right animal for the job might not be available.
In any case, some relevant differences between common riding beasts are given here.
Horses, Mules and the Like
A mule, as the reader will no doubt be aware, is the offspring of a male donkey and a female horse. The offspring of a female donkey and male horse is the much rarer hinny. The Telelelene breeds of mule, donkey and hinny are identical for our purposes. All male mules and hinnies, and most females, are unable to produce offspring.
Horses may go without food for a few days, but must get water every day. Mules and donkeys, by contrast, need food every day, but may go a day or two without water.
Horses are much faster, but also weaker (which is why donkeys are preferred as pack animals), and prone to panic. The 'stubborn' mule, when sensing danger, is likely to refuse to move, whereas the horse will tend to 'bolt'.
None of these beasts should be ridden when they have recently eaten. Strenuous exercise on a full stomach can give them colic, a condition which is inevitably fatal. In the wild, horses graze almost constantly rather than eating 'meals', so that they can safely bolt when endangered.
Note also that, once domesticated, these creatures will tend to eat whatever they come across, whether it be poisonous to them or not, unless their rider or handler is vigilant.
Giant lizards are very placid, and can usually fit two riders comfortably. However they are very slow, and although they can cope with heat very well they may refuse to move in cold weather, or even go into a hibernation-like sleep. This can be fought by the use of certain stones, which can be heated over a fire and then given to the beast to eat. They release their heat gradually and keep the creature warm. The difficulty lies in getting the lizards to accept the stones, and in getting the stones hot enough to have an effect but not so hot that the lizard is injured or made sick.
In addition, lizard-folk believe that giant lizards are cousins to themselves, turned into beasts of burden by sorcery, and so they may lead to unwanted fear and hostility in desert regions where lizard-folk can be found. Giant lizards are most useful in the underworld, where there are less extremes of temperature, few lizard-folk, and where other riding animals may be less comfortable with the frequent darkness.
Camels are, of course, very useful for desert regions, despite their foul temper and low speed and maneuverability compared to the horse, due to their tolerance for heat and ability to go for long periods without water. There are two main species of camel. One resembles the dromedary, or Arabian camel, of our world. The other is similar, but its hump has a tap, allowing it to be used as a source of water. The desert-dwellers who are lucky enough to have domesticated these rarer camels can often be found gathered around one, discussing the day's news.
A General Warning
Given the nature of travel in Teleleli, it should be pointed out that beasts of any species may well ignore their rider when the smell of blood is in their nostrils. There are, of course, 'warhorses' who are specially trained for such circumstances, but they are rare and expensive.