Oh my, be careful, that's an expensive list! And, if my experience is anything to go by, you probably won't want anywhere near all of those while you're in labor. I think most women have a limited period of time in labor when scents (even yummy EO scents) are desirable.
If you have the opportunity to smell any of these before buying them, I'd strongly recommend doing so. Some scents take some getting used to, or they just don't work for some individuals. Geranium oil, for example, is generally considered a good gentle relaxing oil, but it makes me feel sick and nervous. I hate it! Chamomile is nice, but might actually make you too sleepy. And I seem to remember reading that it's contraindicated during pregnancy - don't remember why, though. Citrus oils are all lovely, I use them a lot - but they did NOT smell pleasant to me in labor. Bergamot is my favorite oil usually! And I've never used neroli, but I think it has a lot of the same properties as rose oil.
I'd say you should get lavender and peppermint for sure - they're inexpensive and familiar, so almost everyone can use them. (Watch it with the peppermint, though, too much will give you a headache.) Clary sage was definitely my go-to while in labor because of its pain-relieving qualities. I've been using it to help with menstrual cramps for years and yes, it can also give you a sense of euphoria (though it doesn't hold a candle to, say, IV narcotics...

). If you want to splurge a bit after buying those 3 must-haves, I'd go for a diluted rose oil. It's familiar and delicious, incredibly sexy and feminine, and it makes it easy to do all those "opening flower" birth visualizations when you're surrounded by the scent of roses. Don't feel any need to get the pure rose EO, though, you'll go broke!!!
I'd also recommend buying a cheap candle diffuser on Ebay, or a maybe a lamp ring diffuser - fancier ones aren't really worth it unless you think you'll use it a lot later.
And one last recommendation - I've always gotten excellent quality oils from
Kobashi in the UK - far superior to most of the oils I've bought stateside. You can buy tiny quantities, too, which is good if you're buying expensive stuff or aren't sure if you'll like it. I've been buying oil from them for 10 years; I highly recommend them.
Good luck!!
ETA: I just re-read your post and saw that you're planning to birth in the hospital. They might not let you have a candle diffuser in there (though if I were you, I'd see if you can bully them into allowing it). I know it sounds a little wacky, but I would totally bring a little incandescent lamp in (because I, for one,
hate being surrounded by fluorescents at the best of times and transition is hardly the "best of times") and use a small lamp-ring oil diffuser with it. These are great for three reasons: one, it's really small and portable; two, it heats the oil fairly slowly so you don't overwhelm your senses with too much scent; and three, you get the added benefit of a small, dim light to replace the way-too-bright lights of the L&D room. When I was in labor, I actually convinced the nurses to leave all the lights off and let me labor by the early-morning light coming through the picture window. It was lovely!