Your volume is off a fair bit for us. Assuming you don't reuse them my wife and I will make 8-12 cups a day, which means 350 will last for around 35 days. Or basically a month.
Additionally the filters cost £3.99 as "add ons" at Amazon.co.uk, or £6.99 when purchased alone.
So trade-off is clear one metal filter costs the same as two packets of papers.
(Yeah, tried to persuade my wife to recycle, but she preferred the simplicity of pushing out the puck into the bin, so that was a losing battle.)