No, you don't have to reserve a gift before buying it. Reserving is optional, but it's worth doing — it marks the item as taken so two people don't end up buying the same gift.
Reserving and buying are separate steps. You can buy without reserving, but then no one else knows you've got that wish.
Why reserving helps
Once you reserve a wish, a second person can't reserve the same item until you cancel, which is what signals "I've got this one." It costs you nothing, because a reservation doesn't charge you or place an order — it's just a marker. See "Does Wishpicks process payments?" And the surprise holds: by default the owner doesn't even see that anything was reserved, and your name stays hidden. See "Can I see who reserved or bought a gift?" in Gift Reservation.
Keep in mind
Reserving is not buying. A reservation only signals your intent. You still buy the item yourself in the external store. See "Can I buy a gift directly on Wishpicks?"
One item, one reservation. Each item can be reserved by only one person at a time. If a wish is already reserved, someone else has it — pick a different one.
Do you need an account to reserve? That depends on the owner's settings. Some wishlists let anyone reserve without signing in, some require you to sign in first, and on some reserving is turned off. See "How do I reserve a gift before buying?"
Buying without reserving is fine too. Use the wish's Buy link to go to the store — just know that without a reservation, someone else might buy the same item.
A reservation does not fulfill the wish. You'll need to do that separately by actually buying it, and after you buy, only the owner can mark the item as received. See "What should I do after buying the gift?"