As a permanent resident, you can petition for your spouse to get a U.S. immigrant visa (a green card). But it's easier and faster if you become a U.S. citizen first.
As a U.S. citizen or green card holder, you're free to marry a foreign national or non-citizen immigrant - but you'll need to consider immigration laws to move your new spouse to the U.S. permanently.
You can't lawfully stay in the U.S. just because your I-130 petition was approved. It's only the beginning of a long process to become a permanent legal resident.