Getting your bra size right is a difficult exercise.
The band size is critical, and if you are new to bra wearing it's difficult to realise how snug this must be to get a good supportive fit. On the loosest set of hooks, with new bra, you should only be able to get 3 or 4 fingers under your bra band. As the bra wears, you can move to the next set of hooks.
A properly fitting bra is really firm, and this takes some getting used to! Many lingerie shops measure your under bust size then add 3", forgetting that modern elasticated bra bands are designed to stretch. This is wrong. If you measure 36" under your boobs, then you need a 36" band.
For cup size, the starting rule is to add a size for every inch your across-nipple bust exceeds your under
bust.So if you measure 38/36, you are nominally 36 B.
This is the starting point, and the problem is that manufacturers have different standards for their bras. You may be a 36B with Wonderbra, but 38A with Victoria's Secret.
When you try on new bra, don't forget to "scoop" all your breast tissue into the cup. This can make quite difference, especially with a push-up.
Two tips: a bra is a support garment, and to do any good, it will be tight. Your band will be firm and your bra straps need to be quite snug to avoid them slipping down (do avoid the dropped bra strap!). Your bra will make marks on your back and shoulders. If you take off your shirt, it will be obvious that you have been wearing a bra. I have needed a bra for some time and I carry permanent grooves on my shoulders. But my bra straps locate in them nicely, and this is all part of becoming a bra lamb.
Secondly, bid for used bras on eBay. They are often very cheap and you can experiment with different sizes, styles etc, at low cost.