Hi Mikki! You'll want a nice long thin needle for needle-turn applique. They're sometimes labeled as "straw needles" or milliner's. The extra length is handy because you can use it to turn the fabric ahead of your stitches and finger press as you go. If you can, buy a good quality needle--it's worth the extra cost. As far as size, it's a comfort thing. The smaller the size #, the longer the needle.
Thin silk thread in the same color as your applique will make your stitches just about disappear...but silk can be slippery to work with and the color range and expense can be a problem. If you're working with cotton, try to get the thinnest cotton thread you can. My favorite is a 60 weight thread. Match your applique color as best you can; if you can't, go a bit darker.
Hope this helps! I love hand applique and hope you will as well :D