Apologies, this is a long one! I'll talk you through Ewa once we have some of this sussed :)
Have a look at your breast shape, as this will give some indication of what shapes and brands might suit you. Try to work out:
If your boobs are close or wide set (this is all about the gap between them)
Are your breasts wide or narrow rooted (so how wide is the base of each individual breast, are they mainly on the front or quite far in to your armpits)
Are you fuller on the top or bottom?
How firm is your breast tissue?
If you have a think about that we can advise on bras/brands.
Now, trying to get one to fit perfectly! Things to look at/think about:
Band size: The starting point is that band size=back measurement in inches. This should be a pretty tight measurement, and as a rule of thump most people with an odd measurement get on better with the rounded down number (so most 35s would find a 34 works better than a 36). There are a couple of exceptions though. Very slim people i.e. those with little to no padding around the ribs sometimes need one band size up (should never be more really) and those of us with a lot more padding sometimes need a size which is smaller than the measurement. The reason for this is that the band needs to be a firm support and if you are a little softer sometimes you need to go down to get this support. Also, larger bands can physically stretch further.
Getting the band right is the single most important thing. What I would suggest is when the new bras arrive (or if you have any existing ones which aren't too stretched) then try them BACK TO FRONT. This lets you see how the back fits without the cups distorting it (if you don't have enough cup space the band will feel too tight)
I don't think you will need any bigger than a 36. If anything, you might need to try a 34 in some styles.
Cup size - start with the 36F as you said. When you get a new bra, check the band first. Then, take it off and put it on the right way. I do this by putting my arms through the straps, leaning forward, dropping my boobs in to the cups and fastening it behind me. Then, you need to scoop
Scooping: stand side on to the mirror. Take your left hand, and put it inside your right bra cup. Reach round as far as you can and pull forward all the soft tissue that's bumping out above or below the band, or that's causing lumps in the armpits. If it won't go in to the cup, then you need a bigger cup not a bigger band. Cos we've already tested the band :) Repeat on other side.
Now, stand up and take a look. Sometimes it's easier to do this with a tight t shirt over the top as any quad boob will be immediately obvious in a top (stand side on to a mirror and breathe in and out)
Things you need to look for in the fit:
Where are the wires relative to your boobs - are the resting on breast tissue at any point? on the flip side, do you have a gap between your breast tissue, and the edge of the wire?
Does the cup gape anywhere?
How to the straps feel - obviously you can loosen/tighten them, but are they in a good position or are they too far round in to your armpit?