The tap water really isn't that terrible. I would be more concerned about the gunk that builds up in the water pipes if it is an old house, than the water that comes from the treatment plant. It gets dirty in transit to your faucet (i suppose i'm not helping my case here, but its true!)
Just try drinking tap water with an open mind and save yourself some cash, i haven't died yet, and hey it'll help you build a good immune system
No but seriously, please don't buy bottled water, you're supporting really horrible companies that get it for pennies on the dollar and produce a very non-sustainable product.
As for filters with activated carbon, that's all pretty moot. You should be concerned about biological contaminants (which are picked up by the clean water from the treatment plant, going through the cities dirty pipes) in your water, not metals. Those filters do not protect you from germs unless you're using one that emits UV