We just used BJU's American History. Sd really liked it. We had used Abeka for World History the year before and she hated that. The student activities book for BJU really helped alot too. I had looked at Notgrass and Beautiful Feet but those were too much reading for her. As a former high school History teacher I also think that as a textbook goes BJU's is pretty well set up. I would not say it was an honors book but a good standard History. Their tests are also pretty well laid out. I could not stand Abeka's test and ended up making my own up last year

I have used both Horizons Math and Phonics and love both. That being said I would not push it with a 4 year old. I did not use Horizons k for Math but did use it for phonics. It is pretty advanced. If you are starting with a 4 year old I would say go very slowly or even wait a year.