I'll share our experience, but I'm subbing to learn more--I know I don't know enough.
Our main issue is heavy metals, primarily mercury but my daughter's hair test also came back high in arsenic, and I'm assuming we're all basically the same (we used the hair elements test from Doctor’s Data, ordered through Direct Lab Services). We (my HCP and I) diagnosed me based mainly on case history--timing of onset of allergies, anxiety, later on depression, thyroid and adrenal problems, and the kids were mostly an off-shoot of me not being healthy, with a few red flags like head-banging thrown in (but only for my son, not my daughter, who seems physiologically much more like my husband, though she still has a very high toxic load).
Our allergies/intolerances are minor in the grand scheme of things, just gluten, casein, cashews and chocolate. Those got better in my son with avoidance, a small amount of gut healing stuff (CLO, a fair amount of bone broth for a while, some fermented veggies but not every day) and lots of supps to support detox pathways (the autism biomed approach). I assume that more gut healing stuff would've been appropriate if we'd had more or more severe allergies. My daughter's more prone to yeast and I'm just starting to explore what to do about it, especially since I saw it flare the last round I chelated her and I want to get it under control before doing more rounds.
As a timeline--we started gfcf in June07, and I figured out the cashews and chocolate in fall 07 (I think). In March-ish 08, my son got two separate large gluten exposures and a chocolate exposure, and didn't bang his head on the wall for the gluten (which he had done in fall 07), and got a very, very faint, very delayed rash for the chocolate. I think the healing was mostly due to avoidance and reducing his toxic load. But I won’t add any of those back in til I’m sure we’re done chelating.
Since our gut imbalances seem minor compared to the overall issues, I’ve felt comfortable addressing the detox side first and the gut health second. For people with significant allergies or other signs of gut problems, it seems like working more on those at first would be better. But I don’t really know how much it’s guess-and-check to see what to tackle first, or if some people need to do significant work on multiple fronts simultaneously in order to allow their bodies to start healing.