Need help choosing correct wire to a detached garage
In the current era, for a garage you had better plan a feed that can support EV charging, at least, even if you don't currently plan to do that. You've provided no load information, so picking a wire size is speculative at best.

4 wire is required, barring some exceptions that are unlikely to come into play economically at this distance (such as using transformers for longer distances, but they would not be cost-effective at this distance .vs. larger wire.)

Use conduit (trenches are expensive, conduit is cheap) and put in at least one spare conduit for communications circuits, since (trenches are expensive, conduit is cheap.)

Use a large panel with many spaces - the amp rating of the panel is mostly irrelevant (you can have a 200A main breaker panel and feed it with a 50A breaker - the 200A main is just serving as the required switch in that case.)