The meteorites are rich in metals such as nickel, iron, platinum, gold. Easiest to mine, near Earth nickel and platinum rich asteroids.
Helium 3 is far more speculative and I'm not sure why it gets so much attention. We don't know what will be the best way to do fusion in the future and right now there's no huge market for Helium 3. And requires a lot of mining of the lunar regolith to extract a small amount of Helium 3.
If someone finds another way of doing fusion that works better then it would be valueless (after saturating the market for medical lung imaging and Helium-3 refrigerators etc).
So far we can't use it for fusion power at all. And nobody is working on a helium 3 fusion power plant at present. Just Deuterium - Tritium and commercial fusion power using those also is some decades away probably.
So I think it is rather too soon to start planning for extracting Helium 3 which might be needed by some future power plants a few decades from now, or might not be needed at all depending on future fusion research developments.
As for improving conditions on the Earth, perhaps platinum, very useful metal could be as widely used as aluminium if it didn't cost so much, might be biggest change as a result of space mining, to have platinum used everywhere. Because it's abundant in meteorites if we could only get it back to Earth. But you also have to think about what effect that would have on the world economy and to avoid situation where you have a monopoly of a few companies together worth as much as the wealthiest countries on Earth or more so if you believe the highest predictions of the value of meteorite imports to Earth.
It could be transformative but would need care to make sure it is for benefit of the whole of humanity and doesn't cause economic crises of one form of another I think.
The outer space treaty may give a good starting point as countries agree to explore space for the benefit of all humanity. But what that actually means once it becomes feasible for some countries and companies to mine asteroids and return the materials to Earth - that needs to be sorted out. The platinum they mine is platinum that belongs to us all already according to the treaty. So can they sell it to us, and on what basis? So the lawyers will have their work cut out working out the consequences there, and the decisions made about what is or is not permitted and how it is done may have major impacts on the world economy if they are right about the potential for future space mining.
Right now it costs so much to send materials and equipment into space but as costs go down we may be faced with the need to settle these issues and it may become worth while to mine the asteroids for these metals.
As well as that, you can mine the asteroids for water and metals to be used in orbit. That may be the first market for asteroid miners - given that it costs so much to send materials into orbit - if you can supply water and metals - and maybe 3d printed parts and struts and solar panels or whatever for satellites in space, and space stations like the ISS and space settlements from space mining, that then could be worth doing long before it is worthwhile exporting from space to Earth.
Returning the materials from space to Earth BTW may not cost much, low cost aeroshells and parachutes. Still, early space mining likely to cost so much anyway, that the materials you produce may only be worth buying if you use them in orbit to save costs of transporting them to orbit. So that's why space miners often talk about starting up by supplying water and other ingredients to orbital settlements and satellites.