You should be able to grow a lot of the same plants here that you have in NJ. Our winters are fairly mild but with enough cold temps for plants that need a cold dormancy and we have a nice long growing season. What are you thinking of trying to bring with you? I moved 2 1/2 years ago and I'm still kicking myself for some of the things I left behind.
I have lived in TN all my life and have never seen hummingbirds other than the Ruby Throated. My Peterson Guide to Eastern Birds does not list any other species as regulars here. We have lots of songbirds that you will enjoy, especially if you plan your landscaping to attract them. Audobon.org lists a local chapter in Nashville, that may be a good resource for you.
Looks like you are new to Gardenweb. You may want to add your e-mail address to your member profile. With a new garden you could benefit from some of the plant and seed exchanges available on some of the Gardenweb forums.
Good luck with your move and welcome to Tennessee!
Mechele

Here is a link that might be useful: Audobon site

Another resource to look forward to are the plant swaps. There are Spring and Fall plant swaps in East Tennessee, Middle Tennessee, and West Tennessee. Sounds like the Middle Tennessee Plant Swap will be closest to you, but if you're out towards Knoxville when we have ours, you're welcome to check us out too. I'll attach a link to the MTPS below. The site hasn't been updated, but I think I remember that they have already determined a date for the Spring swap. I bet someone will provide more information when they read this.

Here is a link that might be useful: Middle Tennessee Plant Swap

"There have been seven species documented in Tennessee with two species, the Ruby-throated Hummingbird and the Rufous Hummingbird being listed as regular visitors. The other five species, which includes the Black-chinned Hummingbird, the Anna's Hummingbird, the Calliope Hummingbird, the Broad-tailed Hummingbird and the Allen's Hummingbird, are considered accidental visitors to Tennessee, which means that they have been documented in the state, but they are not commonly seen every year in larger populations."

http://www.associatedcontent.com/article/280429/hummingbirds_in_tennessee.html

Here's a cool checklist of hummingbird species by state, with photos --

http://www.rubythroat.org/ChecklistsUSStatesMain.html

Thank you everyone for your help. Yes, I am new to this site. I will add my e-mail address.

I have some plants in containers that I will be bringing...pussy willow, flowering cherry tree (I think that's what it's called - someone gave it to me), hens & chicks plus I have a yellow butterfly bush I love. There are also several shoots from a bush/tree that for the life of me I can't remember the name!! (Senior moment) I also want to bring some daylilies and irises. I know I can probably get them there, but I guess it's because they'll remind me of here plus they were all given to me by a friend.

Part of me wants to bring everything because I'm afraid whoever buys our house might not be a gardener and then everything will be destroyed. We also have a small pond but I have already decided I'm giving the fish to another friend who also has a pond. We will eventually build another one in TN.

I will definitely check out the sites you all have recommended and again, thanks for your help.