How do I find job prospects in Sweden?

My husband and I are thinking of moving to Sweden in the next 18 months with our two school aged kids. He is an EU citizen so we don't foresee an issue with finding work. What we are having a hard time with is determining how fast and what kind of work he would be able to find. Company transfer isn't an option for either of us. And actually how to go about moving there to begin with. I am an US citizen and from what I am understanding I won't be able to join him at the same time. Is this correct? We are thinking of visiting in the summer to investigate job prospects. Is this a good idea? Who should we talk to while there regarding this? I have family in Gothenburg but they aren't expats so while they offer some help they also don't know much. Any help or guidance anyone can offer is appreciated. Thanks