You could go to 5 different 'bike fitters' and end up with 5 distinctly different set-ups. You need to find someone that understands then type of riding you plan on doing and is comfortable doing fittings for that. Some fitters are very caught up in 'racing' fits and will set up most of their clients in a similar way. I worked with a guy for years that thought every custom frame he did a fitting for needed a head tube extension. I'm surprised that the frame builders would actually make some of these frames. Ask around when you're riding w/ groups, see what others have to say about this. And of course ignore lowrider's advice. If you knew what you wanted you'd just buy it or have it made.
I don't even know what questions to ask of bike fitters. My local shop is run by mountain bikers who are skeptical of the value of a professional fit. I'm in a rural area, and busy every morning and evening. All of my group experience is getting friends of mine to ride midday. The one guy I've ridden with who strongly recommended a fit did his several years ago when he lived in California, and it's not worth a ~4,000 mile round trip to his fitter.
I mostly ride 1-3 hours at a time with occasional longer rides. I like riding pavement, and have quite a lot of nice rural roads to ride, an I hope to get a bike that is capable of venturing onto some of the local gravel roads as well. I like going fast and wouldn't mind trying my hand at some racing, but at 35 and with the natural athletic talent of a pineapple I won't be racing to win. Local hills are mostly in the 2-400' vertical x 0.5-3 mile horizontal range: some punchy climbs, and enough going down that I sometimes spin out in my current top 53x11 gear.
So what kind of riding is that? And barring finding somebody who knows somebody, how do I find somebody who can help me with that as opposed to somebody who just says they can help me?
Sorry for the dumb questions, I'm genuinely a bit confused.