Hi,
I think you can use most of the clothes of your first one if you already have them. Since, your first one is only 13 months, his clothes would be handy and not even worn out. So, the ones that you find are really new, you can use them for the second one. Apart from this, you can buy one or two pair of clothes, vests and t-shirts and pyjamas, mittens, newborn diapers, bottles, wipes towels, bibs, etc. And I suggest, do not buy too many things right away as you can use many things of the first baby.