As mentioned, softies are probably the easiest corals to keep straight off the bat with the exception of some Ricordia (I can't keep a yuma ric to save my life. FL ric's, all day long but a yuma is like lighting a $50 bill on fire).
Mushrooms (including FL ricordia)
Devil's hand / finger leathers
Cabbage coral
Toadstool
Kenya tree***
GSP***
Xenia***
Zoanthids
*** all of these corals marked *** have some caveats. Kenya trees drop 'babies' and reproduce like mad. To the point that you should easily be able to get one for free or VERY cheap. Do not pay much for them. And consider that they can be hard to eradicate and very prolific on reproduction.
***GSP & Xenia as mentioned can over-run a tank if not isolated, so be careful there or at least consider the possibility that your tank could be filled if left unchecked.
Toadstools are awesome because they can grow HUGE and look beautiful IMHO. Same thing with mushrooms. You can get some very colorful mushrooms quite cheap.
All of the above is VERY easy to care for and has minimal lighting requirements.
If you wanted to dabble into stony corals, start with some CHEAP LPS corals like Trumpets / Torch corals or birdsnest. Very easy and minimal requirements.