The example image you've shown matches wing types to flight characteristics. One good thing to consider is how you want your manticore to fly. Does it cruise like a vulture? Hover like a hummingbird?
Since they have a lot of physical characteristics in common with large cats who are hunters, I imagine them behaving more like raptors in the sky. With that in mind, looking at the wing style of eagles or hawks seems reasonable.
As far as size, it is worth considering what the bones of this animal are like. Birds have hollow bones and many other weight-saving optimizations that are not found in cats. Also their bodies are bulkier and less aerodynamic than birds, which would increase drag and require greater lift to compensate.
I assume some optimizations like hollow bones would have to be present in a manticore, unless they are imbued with some handwaverian magic that helps them fly.
For the wing proportions, a good starting place is looking at the proportions of raptors, but then perhaps scaling up to compensate for their bulky manticore bodies.
California condor
- Length: 45in
- Wingspan: 120in
- Weight: 22lbs
Bald eagle
- Length: 32in
- Wingspan: 80in
- Weight: 12lbs
Osprey
- Length: 22in
- Wingspan: 54in
- Weight: 3lbs
Red-tailed hawk
- Length: 18in
- Wingspan: 45in
- Weight: 2.5lbs
Lion
- Length: 6-8ft
- Weight: 300-400lbs
If the lion's weight can be reduced to something proportionate to a bird of its size, then maybe a 15-20ft wingspan will do. But if it still weighs hundreds of pounds, then you're going to need some ridiculous looking wings, maybe even a jetpack.