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Square = Princess cut. Good job already knowing that - it'll make it much easier.
If you're going with a simple solitaire band, you're looking at ~600 for platinum or ~300 for gold.
Gold vs platinum: gold is very soft, and therefore alloyed with zinc and nickel for 14k or 18k rings (24k would be pure gold, way too soft). Platinum is a much harder metal (harder to work with and therefore not used for jewelry until the last 50 yrs or so). "Platinum" rings are typically 95% platinum and 5% palladium or ididium. Platinum is superior to white gold primarily because it (1) won't ever tarnish and (2) is hypoallergenic. The hardness difference isn't a big deal.
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