I'd recommend that when entering product prices they're entered without tax and then you can choose whether to include tax in the product prices when displayed in your templates or not with a simple tag:
If you want to summarise this on the order confirmation page there are tags for that too:
You can pretty much use any of the existing tags and simply append '_tax' to display the tax rates including for sub-totals, shipping, etc.
The only tricky bit I see is the bit where you mention about applying tax rates per product group. In most carts tax rates are applied by country or region so doing it by product group could be trickier. Is there a particular reason for that?
I guess if you know the tax rate for a product group and have a way of tagging it as such (using a category, a custom field, or a custom channel) then you could just use the standard Store tags and then a little calculation to add/deduct the tax percentage.