I think you are going to have a very hard time making one for that low of a price. The steam deck itself is sold at a, in Gabe's words, a "painful" price point; which means either low margins or lost money on every sale. They are working at crazy economies of scale to get the price low, and are using it as a loss-leader for steam games. You will be really, really, REALLY hard pressed to assemble a comparable one-off prototype for anywhere close to their price, let alone under it. If budget is your primary factor, I would advise looking at the used market for steam decks. If the joy of building is the objective, then I would recommend increasing your budget by a few hundred percent. It IS doable, but its not going to be cheap.