It depends on what you're going to do with the mango. Mangos that have been picked in an immature state won't table-ripen but are good for making chutney and relishes with. If you're looking for a ripe sweet mango to eat as-is, look for the reddest ones and then check for meat firmness. Hard ones will table-ripen nicely, and the ones that seem hard but have a bit of give when you squeeze lightly are good to eat right away.
Those that have lost their firmness will be stringy.
You will know that a mango is good for making juice, when you squeeze pieces the skin and it slightly gives a little. You will always know when the mango is bad if the outer skin has a brownish-black color and if there's colored discharge even without pressing.