The cheapest estimate is often the vaguest one, and that's not a coincidence. When a quote doesn't say what's included, everything the painter would rather not do quietly falls outside the scope, and you find out on day three.
First, it should list the surfaces. Not "interior painting" but which rooms, and within them whether ceilings, trim, doors, closets, and inside the closets are in or out. Trim and ceilings are a large share of the labor, and they're the most common thing silently excluded.
Second, the number of coats, and whether primer is included. Two finish coats over a spot-primed, patched wall is a different product from one coat over whatever is there. A color change from dark to light almost never covers in one.
Third, the prep. Patching, sanding, caulking, and priming on interiors; washing, scraping, sanding, priming, and caulking on exteriors. If prep isn't itemized, assume it isn't priced, because on most jobs it's more hours than the painting itself.
Fourth, the actual products — brand and line, not just "premium paint." Fifth, a start date and a realistic number of working days. Sixth, how changes get handled: a good contractor prices a change in writing before doing it, so the final invoice matches the estimate.
None of this is unusual to ask for. We put all six on every estimate we write, free, and it stays good for 30 days. If another quote won't put those in writing, that's worth more than the price difference.