I suspect that each Aromatherapist will have their own list but a good way to start is to look at the student/starter packs that some of the suppliers of essential oils have. The starter pack I have linked to contains the following,
2.5ml: Jasmine Grandiflorum
5ml: Bergamot, cardamon, frankincense, geranium, ginger, sweet marjoram, orange, rosemary 1.8 cineole, tea tree & vetiver
12ml: Lavender true
I would add Juniper as it is one of my favourite essential oils and I would have to have either Roman or German chamomile (both these are included in the next pack up, the student pack) or blue tansy as a powerful anti-inflammatory oil. Another oil I would not be without is rose, both for it’s soothing qualities in dealing with grief, early loss and healing with PTSD but also it is one of the oils useful for menstrual problems along with cypress and clary sage.
However if there is an oil that you find useful that is not in any of the packs, you can always buy that one separately, for example, I often use bitter orange instead of bergamot for depression. Myrrh is a great oil for first aid and preventing infection in cuts as is tea tree. And remember, there is no right and wrong as long as you always dilute oils in a carrier oil before applying to the skin. If you really like the smell of an oil, you can use it in a diffuser or use it in a skin balm etc.
Needless to say, I could probably go on to say something about every oil I have in my collection, (just over 60) at the moment. This is probably overkill for anyone who is not a therapist, so I suggest going for the ones in the starter pack or the student pack on the same site if you can afford that many at once. The alternative is to buy them one at a time. In Cambridge where I live and practice, Oshadi do an organic range and you can pick them up if you live close rather than pay postage!