Personally, I don’t like baseball caps, as they are designed for forward vision, and I find the peak comes too low at the sides, obscuring my lateral vision.
For summer I tend to use an ordinary cycle cap, but I avoid the ‘one size fits all’ types and go for something a bit more fitted. I have had good experience with ‘Smith London’ caps.
For winter, I have tried a variety of things, but the best so far I found in Ireland: a lined tweed ‘jockey cap’ type with fold down ear flaps, by ‘John Hanley’. With the flaps down it is very secure, very warm, and quite water resistant.