My daily driver for charts is Luna Astrology. I use Astro Gold if I want to do a tri-wheel, but Luna is much prettier and easier for daily use.
Astro.com is a great free site with tons of options. I use Astro-Seek.com if I want to do progressed composites, as neither of the above tools will do these.
Here are a few astrologers I recommend who have training programs to learn astrology.
Besides the above teachers, here are some other astrologers I watch to learn and keep up on the AstroWeather: