GOod question, I've never exactly worked it out. There are a lot of variables, like whether your water is metered or not, and how warm your house is.
Bigger tanks are more expensive to run. The cheapest option would probably be a 60 litre unheated tank with minimal lighting (lots of plants only need a bit of lighting) and some white cloud mountain minnows.
You could have no lighting, but you wouldn't be able to see the fish very well which would kind of defeat the purpose of having a fish tank. Some of the newer LED lights probably use a lot less power but they're quite pricey.
A filter is absolutely necessary and shouldn't be turned off, except for cleaning, so there's no corners to be cut there.
Set up can be done very cheaply, I've set several fish tanks up for free. You just have to be cheeky and ask around, try freecycle, Facebook etc. Someone's always got a spare fish tank in their shed or loft.
This is a good run down of what equipment costs how much. It's an American site so the gallons are wrong different but you get the idea.
There's also the water and the dechlorinator to take into account, but that's not much. I get a big bottle of dechlorinator for about £20 and I'm sure it's lasted over a year, and that's with more than one tank.
Cheapo tanks can definitely be done, but don't cut too many corners because if your water quality suffers due to skipping water changes or having a filter that's too small, your fish will get ill and you'll end up forking out for all sorts of medication.
Hope that helps :)