Pierre
You won't go wrong if you just duplicate the dimensions of your current barrel.
One tip: if you want to black your barrel then you need a decent finish. You need to first turn it down between centres using a steady. Then centreless grind it to size and then polish it. Don't be tempted just to centreless grind it because barrels are invariably not concentric, and if your breech is out then you may well get puffing.
Another tip: when you drill the small blind hiole for the barrel locating grub screw which goes through the forward scope mounting hole, use an endmill so you get a flat bottomed hole. This makes is easier to adjust and there will be no tendency for the tapered point on the grub screw to centre in the hole, thus pulling the barrel out of position.
HTH
Andy