You're right that handstitching is better, I use my machine to hem basic things like casual cotton skirts and jeans, but nice dresses look a lot better with an invisible handstitched hem.
My process for hemming delicate fabrics:
1. pin to desired length (ideally have a friend do this while you are wearing it), measure out 2"-4" extra for the hem, and cut off any extra length.
2. Gently iron on medium heat to set folds, and if needed adjust the pins so that the fabric is even and smooth around the whole hemline
3. handstitch hem with invisible stitch (a youtube search will turn up lots of how to videos for this stitch, it's not difficult, just takes some time). I usually space my stitches 3/8" to 1/2" apart when invisible hemming.
For needles, I use whatever I have around that is reasonably fine. I don't bother with basting, I feel that pins work fine for me to hold the hem in place as I'm sewing.
If you are new to this, I would suggest saving fabric from the extra length you cut off the dress and practicing an invisible hemstitch on the extra fabric. That way, if you do make any mistakes they will be on scrap fabric, and you can figure out what you are doing wrong and fix it before moving on to your dress.