Going by her previous wishlist she is most definitely sensitive skinned, so I'd suggest going the mineral oil-, fragrance-, and silicone free route for this. The moistfull line from Etude House and Laneige mask are sort of out of the running as a result.
Oil cleanser - I'd go for the Heimish all in one balm, it's somewhat similar to the EH Cleansing Balm, samples here but you can get the whole product for not much more here.
Second cleanser- If you can splurge a bit I think the Su:M 37 Rose Cleansing Stick is probably a good one for sensitive skin lowest price I could find it, full size not a sample to be found. Someone else may have a better suggestion, but I have had a hard time finding a nice one without SLS and fragrance that isn't completely utilitarian and a bit boring.
Hydrating serum- Mizon Hyaloronic Acid Serum on ebay but also available at Jolse if you prefer to shop in as few places as possible (with slight price increase but Jolse flood you with free samples). Full sized product again as I can't find a sample version.
Essence- Benton Essence (+ a cream) as Aurora mentioned, both look good for sensitive skin.
Moisturiser- there's a moisturiser in the Benton offering but my sensitive skin really responds well to this Japanese lotion and it also looks beautiful in its packaging (much better than on the pics), it sits somewhere in between a moisturiser and hydrating essence and makes for a great layering product for a moisture boost, but again no samples so stretching the budget a bit here.
I'll have to get back to you on masks, the fragrance free ones are difficult to source per piece at the moment. I was going to suggest the Missha FTE but it's been reformulated (for the worse) so I'll have to think of a suitable alternative.