The following is a rough guide to what is commonly available, at least in the UK. There is probably a wider range of species available in North America or Germany and the Netherlands. The latter two countries in particular do a lot of captive breeding of the rarer species. It should be remembered, by the way, that many species are covered by conservation laws to a lesser or greater degree. Commonly offered species should however require no paperwork, apart from tortoises, which in the UK at least should be all be bred from existing captive stock.
Since I have personally kept no chelonians since childhood, what follows are observations from specialist and general pet shops, advice from people better placed to know than myself, and a lot of reading. If you like, it should be considered the general consensus, although some people may disagree with some of the observations. There is no real saying which is the best tortoise, or the best pond turtle, but there are species which are either easily kept and readily available or which have a reputation for being difficult in one way or another or whose expense could not be justified by a first-time buyer.
Let's have a look at tortoises first. In the UK, the most commonly seen are Hermann's Tortoise, Testudo hermanni, and the Greek Tortoise (Testudo graeca), followed by Testudo horsfieldi, the Russian or Steppe Tortoise. Expect to pay no less, and usually more, than £100-£150 for one from a reputable breeder or seller. Captive-bred hatchlings are often available but will require more attention and should probably be kept indoors until a suitable size. There is usually a reasonable amount of information on the correct care of these tortoises, and they can be kept out of doors for about half the year. All of them hibernate during the winter. Testudo marginata is much more rare but can be kept more or less like the others, while Testudo kleinmanni adapts badly to our climate and should not be considered as a first or even second pet tortoise. When acquiring a Testudo species, please make sure you buy an up-to-date book on their care. Our knowledge of their care requirements has come a long way in the past thirty years.
Other tortoises sometimes seen are Kinixys or Hinged Tortoises, which are from central and southern Africa. As a rule these have a reputation for being delicate, and some species adapt worse than others. They are omnivorous. Some like dry environments, while others need constant humidity and a lot of vegetation cover. Going up in size, Leopard Tortoises (Geochelone pardalis) and Sulcatas (Geochelone sulcata) are also available, but these grow large, especially the Sulcatas, and really require enormous enclosures or else the run of the garden. They are not the most practical choice for a cool climate, but keepers in the US may be well placed in this respect. Geochelone tortoises, including the popular Red-Foot, are now captive-bred and sometimes available: they are apparently less difficult than some of the African species. The diminutive Pancake Tortoises (Malochercus tornieri) would probably make excellent pets for many people, being small enough to keep in a suitably-sized vivarium, but unfortunately overcollecting from the wild has made them scarce and they are now protected. The few that are bred now are best left to people with the experience to keep breeding them!
Asian Tortoises are rarely seen in the UK, but the Burmese Tortoise Manouria emys is supposed to make a good pet.
Originally the Red-Eared Slider or terrapin, Trachemys scripta, was commonly imported into Europe and the UK as a pet. However, a number turned up in ponds and rivers outside their native country and thus the species came to be regarded as something of a pest. This may or may not have been the fault of Ninja Mutant Turtles and children demanding a terrapin from their parents, but now it seems that few shops stock them. However, if you do want one, you can probably get one (or more) from an animal rescue centre if you offer to rehome them (ie give them a good home). They are quite hardy and books on their care are available. They can be kept outdoors most of the time.
From Africa comes the Helmeted Turtle, Pelomedusa subrufa. This is a rather flat-shelled species which draws its neck in sideways, thus always keeping one eye on the situation, so to speak. It is not large and has a reputation for being intelligent and hardy. Its main drawback is its stink, which is the main reason few Africans will eat it. It has been recommended by different writers as a good pet.
Most other turtles seen in the UK trade at least are from Asia or America. Many of them are small and hardy, so will either live fairly well in a good-sized tank or else be tolerant of life outside. The North American ones tend to be of the Kinosternon or Sternotherus species, the so-called "Mud" and "Musk" turtles (the musk being an unpleasant odour produced by the turtle should it feel threatened). Although plain brown in appearance they are hardy, and again information is available on their care. The Asian Chinemys reevesii has been recommended for similar reasons (size and toughness) as a good turtle for beginners, and for the UK have the added advantage that they hail from climates with cold winters (China and Japan). The Painted Turtle, Chrysemys picta, is another choice in this category. Information on Asian turtles is less widely available and there do appear to be a greater number of species, but the information is available nevertheless.
The European Pond Turtle, Emys orbicularis, is sometimes available and again can be kept outside for much of the year. Unfortunately there is not much in print on its care, but a bit of research will turn up some useful guides.
Worth discussion are the so-called Snapping Turtles of the Americas. These are two rather prehistoric- and almost brutal-looking species that attain large sizes when adult. The Alligator Snapper is protected and rarely available in the UK, but Common Snappers can be obtained. They are tough but have a fairly aggressive temperament so are not a pet in the tortoise sense of the word. If kept in either a large enclosure or, better, in a suitable pond outside, they usually do well. They rarely leave the water.
Soft-shelled turtles are sometimes offered for sale, but are really for specialists only. Their snappy temperament, need for clean water and non-abrasive surroundings, and habit of burrowing themselves into the sand are probably disadvantages in the eyes of most people.
The matamata (Chelus fimbriatus) is a bizarre-looking aquatic turtle from South America which has strict requirements about water quality and is probably best left to experienced keepers. Likewise, the Map Turtles (Graptemys) of North America require scrupulously clean water to do well. Most of the side-necked turtles from Australia and South America are either unavailable or have little information on their correct care readily available, and again are probably best left to specialists. South American turtles of the genera Peltocephalus and Podocnemis grow to large sizes (at least 30cm/1', and in some cases much more) that make them impossible to keep for anyone who cannot spare the space for a very large heated tank