For competitive players the Staunton design is kind of the gold standard. Generally you are looking for a 3.75 inch King. Serious players usually hate funny looking or novelty type sets even if they are luxurious. This is above your budget but is a Staunton design and the same pieces that were used in Fischer Spassky world championship match.
https://www.regencychess.ca/chess-sets/fischer-spassky