Is a first order discount automatic, or does the customer have to type a code?

Either, your choice. For a code, make a coupon such as WELCOME10 under Marketing → Coupons and put it on your page and your flyers; the customer types it at checkout. For no code, open Marketing → Offers and add a rule of the First order welcome type: a customer who has never ordered from you sees the offer on the page without typing anything. Both are checked again on our side at checkout, so an expired offer can never be charged wrongly. The automatic one converts better because there is nothing to remember, and the code is better when you want to know which flyer worked.