in a small tank you can get away with a hob filter . the biggest thing that you would need would be a good light to support corals , a pair of small power heads for circulation and a decent skimmer, you would need sand and rock you also are going to need to do a cycle .
in a ten gallon tank you would be limited to certain fish as theirs not really a big selection that would work in a tank that size.
as for coral it would depend on what you like some coral grows fast and will need constant trimming , I myself always wanted to start a 10g zoa garden no fish just a few small inverts something easy to maintain .
not knowing what your wanting its hard to get going in the direction you want to go , everyone has different ideas on what they expect from there tanks , so some input on your end helping us guide you on the right path .
there are lots of different types of coral that would work in a 10g with out over growing the tank , knowing how to frag out corals that start growing out to much trading them for others you wanted .