Start with the problem
Do not buy a Wi-Fi product just because one room has poor service. First establish whether you have a coverage problem, an internet-speed problem or interference/congestion.
Access point
If Ethernet is already available near the weak area, a wired access point is often the cleanest way to create strong Wi-Fi there.
Mesh
Mesh can be useful when you need coordinated coverage across several areas and running Ethernet is difficult. Wired backhaul, when available, can improve the design.
Extender
An extender can solve a modest coverage gap, but placement matters: it needs a usable connection to the existing Wi-Fi before it can repeat it effectively.