What's the best option with a $250 budget?

I don't know dick about catcher's mitts, but I can recommend Just Gloves & know the reputation of the brands fairly well.

Top of the budget:

https://www.justballgloves.com/product/wilson-a2000-superskin-m1d-33-5--baseball-catchers-mitt--wbw100401335/34687/

https://www.justballgloves.com/product/all-star-pro-series-baseball-catchers-mitt--cm3100sbt/7957/

If you want to go a little cheaper, Easton doesn't make gloves anymore (Rawlings owns them) so they have some close out deals that are very good.

https://www.justballgloves.com/product/easton-professional-collection-34-baseball-catchers-mitt-pck-h40/36603/

https://www.justballgloves.com/product/easton-professional-collection-hybrid-33-5--baseball-catchers-mitt--pch-h35/34405/