What is the best shop to buy weapons on AQ Worlds

"Best shop" is relative and there are different ways to answer.
For "cool" member and non-member items, the Suggestion Shop is the best. It is frequently updated and has items for all tastes, classes, and looks.

The Suggestion Shop is located in Yulgar's Inn (/join Yulgar).

For rare, one-of-a-kind, and most likely never-to-be-seen again weapons, check to see if there are any special events going on. For example, Frostval, Summer Time, Canada Day, Cinco de Mayo, and so on, will have special items for members and non-members alike.