On a Budget.. and for those just starting out. What do you think are MUST HAVES???

Depends what your shooting.
Simple things first.
I have UV filters on all my lenses. This is just a protection practice. 3yr olds have fast sticky fingers.
Lenspen!
http://www.bhphotovideo.com/c/product/507196-REG/Pearstone_LENLP1_LP_1_Lens_Pen_Black_.html

I suppose my girls will be the most things I'll be shooting. But enjoy shoting all kinds of things. As you can see from me taking pics of DH.

I don't think you'll get much use out of a tripod. They're mainly when you need to keep steady and have a subject that will remain still for a while.
Since you have a Nikon I won't try to sell off my 28-105mm USM so I can get my 100-300mm USM.
I would recommend a decent zoom range. The 28-105mm for me is great for my backyard shots. I can go wide quickly or zoom quickly without physically moving.
Image Stabilization really is essential if your using a big zoom with slow shutter speeds. A good rule of thumb is that your shutter speed should be no slower than your focal length to reduce camera shake. IS can help though. I would go with a lens that has good AF. Canon has USM - Ultra-Sonic Motor, Tamron has HSM - High Speed Motor. Not sure what Nikon has.
If you need to zoom in farther just remember you can crop in on a shot as well.

As far as lenses go, I'm looking at getting the 55-200mm Lens. But not right now. I did find some on craigslist, but not sure if I should go that route... I hope you don't mind all the questions. I'm all over the place on here!!!

Not at all. I was all over the place with questions at first too.
When you get to a zoom range your looking for do some searches and reviews. You can also go to flickr and do a search for that lens and see sample pictures. Some even do specific examples of focal length on one subject.