Regarding "burning snow":
Yeah, "burning snow" sounds like a joke, but it's not. Cameron's advice is right on the money.
What really happens is that the snow wicks up any liquid water created by melting, leaving a small airspace on the bottom. It's the pot that scorches by overheating, and when you finally get water it tastes like something out of the exhaust pipe of a Chevvy. Easy to do with blowtorch-hot backpacking stoves.
I've also noticed it's best to dig down for denser snow/ice. Pouring fresh powder snow into a pot is like pouring sand down a rathole.
Regarding "big mugs":
I strongly agree -- this is critical gear, even for short day hikes and vehicle kits. I've used stainless steel and enamel ones. Stainless lasts a lot longer, and they're making it thinner and lighter these days, which encourages packing one along with you. The enamel on cups these days is pretty sensitive to chipping -- not like the bombproof stuff your grandparents had around. But it still gets the job done.
A mug does more than boil water. I have had many a "cup wash" by adding a little liquid soap to an oversized mug of warm water and pouring it over my head etc. Then I pour some rinse water from my main supply. Never underestimate the boost to morale and good temper that a cup wash can bring.
I have occasionally packed a Sigg aluminum 1-litre fuel bottle in go-fast kits. It's dual purpose and very lightweight. You can boil water in it, let it cool, and then seal it up for travelling. I wouldn't use it except in an emergency, though. You never know what trace materials might leach out.