You wont find a nice wooden set for under $50...
What is the official size of board and pieces in FIDE games? And which brands manufacture the sets?
Here are the official regulations on size
https://handbook.fide.com/files/handbook/C02Standards.pdf
The king should be 9.5 cm high.
4 pawns should fit on one square.


If you want a nice set under $50. I recommend choosing by weight over material. The quad weighted The House of Staunton - The Collector Plastic Chess Set pieces are marvelous.
When I played tournaments in the 80's the board size was 2.75". My king 4.5 and base about 2".
I recently bought the same set/style in a smaller size as a gift. These are name brand, House of Staunton, quad weighed Collector series. These come in 3.75" (51 oz and $44 + tax) and 4" (56.1 oz and $47+ tax) sizes now.
You can use them at home (my box and board cost more), they travel well in a bag. You can't hurt them. They look good, and feel fantastic. They are a joy to play with.
I count myself lucky to have the discontinued 4.5". I will have to weigh them to see what they are. I'll guess 60 oz or more. The feel is better than any other set I've played with.
Buy them on Amazon, as House of Staunton shipping is quite high.
I prefer the natural and black colors. White is ok, but not as pleasant to look at as the natural wood color.
(Reasonable price = under $50)