The other answers have suggested a lot of particular references, many of which are excellent. I'd add, speaking as a math professor: don't worry too much about

The other answers have suggested a lot of particular references, many of which are excellent. I'd add, speaking as a math professor: don't worry too much about holes and lack of intuition. The more you learn, the bigger you will feel like your holes are! Whatever you choose, in my opinion it should involve solving lots of problems. Subject to that, I'd recommend simply that you dive in to any math subject that attracts your attention.