What do I do when my mech is destroyed?
Playing as D.Va, my mech got destroyed with no progress towards getting a new one.
Since D.Va outside the mech has low health, no abilities, and a weak pistol attack, is it even worth trying to fight on foot? Is it ever better to just kill myself to get a new mech and, if so, when?
When your Mech is destroyed you run behind the rest of your team. You're weak, but your pistol does have some range to it. You should pepper the enemy team with shots (each shot SIGNIFICANTLY charges her ult) without taking any chances (Since it's only 30 seconds at most until you're able to suit up again).
To that end, here are the key points:
Try not to lose your mech when surrounded by the enemy team. Easier said than done, I know, but D.Va has great mobility. Try to make your mech last as long as possible by intelligently using her defense matrix.
You're vulnerable WHILE suiting up. Don't suit up in the open or in the middle of a fire fight.
Conversely, she has brief invulnerability when losing her mech. Try to get away ASAP.
She's a tricky hero, but she has a ton of control over when she engages and how she mitigates damage. You can extend her Mech's life and play conservatively (but not timidly) as a pilot to get back into your Mech.
D.Va's pistol is pretty decent, so if you're good at getting kills with Mercy you should be able to get kills with D.Va mechless. Worth remembering that both D.Va and Mercy's pistols are fully automatic, you can just hold down the fire button.
The question you have to ask is which is better in any given situation, putting shots downrange to disrupt the opposition, or wasting ~10 seconds + the run back to respawn with more firepower.