approximate cost - depending on what you pay for the filament - around 5 pence, 7 cents or 6 euro cents.

Any 3d printer will do the job.

Now to the reason you won't be 3d printing phone cases.
1 phone case will take around 1-2 hours to print at a good quality.

Now what you could do, is use the 3d printer to make special customised cases - but it can't and won't replace bulk phone cases, just takes too long.

printer wise - you could spend £400 and get a wanhao duplicator i3 plus, or £300 and get a makerbot replicator clone, or you could spend £10,000 and get an sls machine that prints with nylon.
Or spend £100,000 and get a full colour, multi material all singing and dancing industrial machine.

3d printer prices vary from under £200 for kits to over £300,000 for top of the range industrial machines - and more if you want to print metal objects.

I can't see you selling a customised phone case for enough money to make it worthwhile. But who0 knows, you might be able to :-)