Three sheet options. Letterhead has a constraint no other stationery has (it must feed through an office printer and take toner without lifting) which rules out heavy coated stocks entirely. Filter by sheet size.

8.5″ × 11″, everyday correspondence and invoices.

8.5″ × 14″: contracts, filings and agreements.

Your sheet and format: a4, folded or presentation weight.
Uncoated bond or text around 100 to 120gsm is the working range: substantial in the hand and reliable in a feed tray. Coated stock is not a premium option here, it is a malfunction. Toner does not bond to it and the sheets slip. Where a premium impression matters, it comes from the stock texture, a blind emboss or a foil element at the head, all of which leave the writing area fully usable.
Design the empty space as carefully as the printed part. Letterhead is a background that something else prints on top of, so it needs a generous, genuinely usable correspondence area, and anything sitting where an office printer cannot reach gets clipped. Order envelopes and second sheets from the same batch: paper whites vary between runs, and a mismatched envelope undermines the letter it carries.