The evolution you describe sounds very similar to that of humans, but that doesn't mean it has to look human-like.
When the species leaves the jungle (or the jungle disappears) your species has to find new sources of nutrition. This would influence their physical form the most.
If they dig for rodents, they would develop strong front paws with long, thick claws. If they hunt for big animals, they need to develop pack behavior and therefore communication via poses or gestures (tails or distinct markings on the body could come in handy). Hunting small animals requires a lean build and strong legs. Or they start on their way to higher intelligence by digging traps and laying in wait.
Becomming omnivorous - which influences the dentition - can secure the survival of a species in hard times. There's a consens among scientists that herbivores do not consume the amount of energy needed to develop a big brain and higher intelligence.
The first thing to become obsolete is the tail. In flatlands there is not much use for a grasping tail, so it would probably become thinner and shorter. If it's not used for communication, it could disappear over time.
Upright walk in humans was caused by the need to see above tall grasses and by a slightly lesser energy consumption compared to quadrupedal walk. You don't have to make your species exlusively bipedal, but having hands free is essential for the development of tools and technology. The grasping tail would probably be an inferior substitution for hands.
After that, it's a question of environmental influence. A hot and dry climate would influence the skin and fur differently from a mild or humid climate. Challanging conditions like many poisenous or otherwise deadly plants and animals would drive the development of intelligence or highly social behavior with specialized roles. Lack of nutrition would favor the development of small bodies, while the appearence of big predetors could favor strong builds or fast runners. Sticks and stones would be the first tools to defend against predators.
However you design the environment of this species, keep in mind that traits that no longer necessary for survival disappear over time.
- No brances to grasp, no grasping tail and less agile feed and toes
- no biting prey to death, smaller teeth and smaller protusion of the face
- no harsh weather or development of clothing leads to less fur