The purchase of long guns is not too much of a problem. You go through the procedure of getting a firearms I.D.card. The procedure is basically a background check. The card is a lifetime purchaser I.D. and you present the card when buying a long gun. Generally a drivers liscence is needed for I.D. As you can see there is no problem for long guns. Pistols are another matter. You have to get a pistol purchase permit which when issued allows you to purchase two handguns within I believe 60 days. Depending on where you live this can take from several weeks to 6 months or longer. Where I live I can get a permit in about a month. Some hard a$$ police chiefs might not issue you at all. Getting a carry permit can be almost impossible.
I lived there long ago and am happy to have left, for good. I applied for a permit purchase and the as...le police chief grilled me for about 15 minutes about why I wanted to buy a model 66 sandw. After putting up with his nonsense for ten of those minutes, I said because that is the stainless model of the sandw 19 I carry at work as a fed. He reluctantly signed.
I do not ever wish to be in that position again.