It sounds like you want a "performance" fit. Make sure the bootfitter removes the liner, leaving the plastic shell empty, and has you put your bare foot in there. The bootfitter needs to look at three dimensions of the shell and see how they match your foot: how long the boot is compared to your foot, how tall it is over your foot, and how wide it is. Consider a pencil thickness behind your heel to be a high end performance fit. Two pencil thicknesses may be OK, but not more than that. Width and height gaps should be similarly small. If the bootfitter does not do this shell fit when you ask for a performance fit, leave the shop. He doesn't know what he's doing or he doesn't respect your request.
There should be not much wobble room in any of those three dimensions. Different boot shells are made with different shapes. The bootfitter is there to find the shell that comes closest to matching your foot's anatomy, so a shop with a lot of stock is most likely going to have a shell that comes close to your foot. When the liner is put back in, it will fill the empty space and compress your foot at first, before it gets permanently compressed (packed out) from heat and use. So your boots should feel on the tight side when you buy them... IF you really do want a performance fit. After wearing them for a while they get less tight. "Snug" is the word people usually use for how a performance fit feels after the liner gets packed out a bit.
Any adjustments that happen later, at a price, by a different bootfitter, should be to deal with a boot that's found to be too tight/small in spots, not too big in spots. Your performance fit means the boot is not too big anywhere. The bootfitter can stretch the plastic or grind depressions in the inside of the boot's plastic to make room for bulging bones in your foot, or a big toe that just isn't happy, or ankle bones too high or too low for the built-in ankle-pockets, and so on. Buckles can be moved. Most boots are designed with these adjustments in mind; you can ask about that when you are getting ready to select one.
If you have one foot significantly larger than the other, fit the smaller foot. The bootfitter who makes custom adjustments will enlarge the boot for the larger foot.
If you go with a comfy boot which offers a comfort fit, then when the liner gets compressed, you'll still need bootfitter adjustments so you won't be skiing around with a sloppy boot, which means out-of-control skis. That will involve glueing foam inserts inside the boot to fill the spaces. The cost is not so bad when you need this, but the effectiveness is not so good, because those inserts are squishy and thick. That makes your foot/boot interface function like a loose steering wheel. Another option if you end up with boots too big is to buy an after-market liner whose purpose is to fill the gaps. This can work if the gaps are not so huge, but it is not cheap.
As for flex, it can be softened, but not stiffened. Keep that in mind. Do not buy a soft, soft beginner level boot. It's easy for a bootfitter to soften a boot cuff's flex. There's a temporary way (removing screws) and a permanent way (cutting divots). That can wait until you've skied the boots for a while. A bootfitter cannot stiffen a boot's flex.
Wear very thin socks when you get fitted.
Best of luck in finding what you want.