Bhai, I have first hand experience of many years of each of these cars except Cuore, but also have some experience of driving friend's / relatives Cuores.
I'm not showing off, just giving you confidence to believe in my suggestion. To me you have an almost good enough budget and since I know all these cars pretty well, the choice is clear to me.
Your best choice is to get an Alto. Jitna bhi naya model tak aap kay budget main milti hai lay lo. Checking condition / price etc is your responsibility but here are the plus points because of which i'm making this recommendation. Hope this clears up your mind and makes the choice easier.
Alto has better and bigger interior space than Cuore & Mehran
Alto has good rugged and bigger engine (1000cc)
It will easily manage 120-130 on petrol and 110-120 on CNG on motorway
It has a good AC
It has good mileage on CNG
It's exterior and interior looks are much better than Mehran / Cuore
It's small / medium in size so you wouldn't have any problem parking / reversing or moving through crowded areas and small inroads.
Only bad points are fuel mileage on Petrol isn't good (approx 10-11 km max)
Sometimes self takes long tries to start.
None of these issues is a dealbreaker. Self ka problem aadat ho janay par aur practice say theek ho jata hai, aur petrol par zyada chalana hi nahin.
Even though I have tried my best to convince you, do share at the end which car you end up buying and remember, getting the right condition car in the right price budget is your responsibility. So don't hurry into the purchase decision when you find a car.
I never type such long replies and suggestions, but since you have collected your money over a long time, i'm trying my best to get you to spend in a worthwhile manner.