In terms of appearance, X20 is beautiful and compact, NEX series feels a little ugly but relatively light, D5200 is a standard SLR model, which is for sure, but it has the best sense of operation.
X20 is the cheapest, and 5R and D5200 should not be much different (but the price of SLR depends on the specific lens).
In terms of image quality and cost performance, you should choose 5R or D5200, but X20 is absolutely enough for daily photography, and it is the most convenient to carry, and it is quite suitable for girls who do not intend to study photography in depth.