Fellow small-kitchen apartment noobie here.
I'd say what you NEED is:
1) a microwave, if your new place doesn't have one
2) a toaster oven (does double duty for a toaster, plus can be used to reheat stuff like pizza things you dont want to go soggy faster than I real oven, make garlic bread, etc.)
3) a hand mixer (baking, mixing etc. If you want to do the milkshake/smoothie route get one with an attachment for that and some giant glasses. if you end up using that a lot, then you should think about a blender. we have yet to buy our blender)
4) slow cooker (the only brand name rec I have is get a Rival. They are nigh impossible to kill. The mechanical hand-me down I use with just one knob on it is about 15 years old and still going)
If you have the space after you move in, I would consider the rice cooker/steamer. Or rather, a steamer that can do rice so you can double duty. But those are big, and if you don't have a good place to put it, you won't use it because it will be a pain to get out, which has happened to me.
I think those 4 are the basics. After a month or two in your kitchen it will be all organized and you'll get a better feeling of if you really need something, like if you find the spare time/desire to juice things, and you've noticed there is a space in that one cupboard it could go in... that sort of thing
Also, invest in GOOD pots and pans. Don't get the cheap crap if you can help it, I would personally buy expensive pans before anything else. Good pans will go further to making your cooking pleasant more than any appliance ever could. Crappy pans and stuff will burn, cook unevenly, and you'll spend all your money on takeout instead...
