Can confirm that:
1. A check in your name is best.
2. Opening a business account is second choice, due to the higher fees. As mentioned, in most states if your business name contains your last name, and your business, then you do not need a Fictitious Name License. E.g. "Smith Landscaping" does not need a license, but "ABC Landscaping" would. You would also need a Fictitious Name License if your business name implies other owners/parties, e.g. "Smith & Sons Landscaping," "Smith & Co. Landscaping." So keep it simple. As a sole proprietor, you can use your own SSN as the tax ID, which will keep taxes simple.
I would not get the gift card. $250 you can only spend at one place, vs. $250 you can spend (or save) anywhere?