Hahaha congrats! I have an Ai, and I love her to bits. She's the lady in my avatar picture.
The delivery time depends on a few things, such as the company's current workload, and if you ordered her through a dealer, or directly from ResinSoul. It can be anywhere from 4-10 weeks, with the average being about 6-8. (It's faster to order through RS directly, but the shipping cost is usually a good bit more)
Ai can fit into a large 7-8, or a small 8-9; the ears make it a bit difficult for larger 8-9 wigs, but using velcro and/or a wig cap helps loads. I have a large 8-9 on my Ai, and I have velcro in it, and I snipped tiny slits in the sides to fit over her ears. If you do that, BE CAREFUL! You don't want to snip the hair wefts. If you do end up cutting a weft by accident, don't panic... put a dab of glue on the cut part, and then leave the wig alone til it dries completely, so the weft doesn't unravel, and so you don't get glue all over it.
You can find lots of information on caring for resin dolls in the dollieh maintenance section.
I'll leave the differences between vinyl and resin to someone that owns both, but my general understanding is that vinyl dolls pose better, but stain more readily.