Since you will be qualified to mix up EO blends, I'd suggest get jojoba as the base oil, no allergy concerns, washes out of everything easily and leaves people with a sheen rather than oily, and then take a few EO blends. Taking a lot of individual EO bottles gets to be a pain, so a few good blends are better. I have a few 25ml bottles I fill up with plain jojoba, and another 50ml bottle of jojoba I take, plus the EO blends. I open a 25ml bottle, add the required drops of EO and use that bottle on the client. If they have very dry skin and need more jojoba, I'll just pour a bit from the 50ml bottle in the 25ml bottle and it gets a faint blend note to it. At max, I would do 4 mobile calls per day, so I'm usually just carrying 150ml of jojoba in 5 bottles, 5 EO blends (similar to Sue CarberryF's list, though I carry one bottle of ginger CO2 EO rather than tiger balm), and generally one facial oil blend if it's massage appointments; I've got EO facial blends too (sensitive, oily, calming, etc) I will take if it is more face orientated, those I will just put one drop EO blend in my hand with enough jojoba for the face. This makes carrying the oils MUCH easier. I used to carry a big box around of EOs and various base oils, but it just got too much with everything else. If I am seeing someone that needs something a bit more specific, I make sure to take the specific oils the next time I see them, but for at least 95% of mobile appointments, a bit of a jojoba, a few good quality EO blends, and ginger EO, covers everything the client will need. Even for clinic appointments I tend to mainly use the EO blends these days.
(I've got massage, aromatherapy and beauty training)