As long as you stay away from NPS species, you should be able to keep most LPS and soft corals IMO. I guess it depends on your lighting though, but most do not require exceptionally high light.
LPS-
Torch
Frogspawn
Hammer
Acans
Duncans
Blasto
Chalice
are all considerably easy IMO.
Brains
Scoly's
Plates
Still pretty easy to keep, some can be finicky I suppose.
Alvepora
Elegance
These can sometimes be hit or miss
Goniopora
One of the hardest LPS to keep, however, if you get one of the ORA specimens it should be considerably easier.
Soft corals-
Toadstool
Kenya Tree
Colt Coral
Sinularia
Mushrooms
Zoas
Clove Polyps
Star Polyps
Yellow Fiji Leather
Xenia
Devils Hand
Finger Leather
Anthelia
Cabbage Leather
All really easy to keep, there are some species that are a bit more finicky than others but generally speaking, not hard.
SPS-
I know you said only LPS and Softies, however, should you want to try one, start out with a monti cap. They are very forgiving compared to other SPS, and they can really stand out in a mixed reef.
Before purchasing anything, be sure to research for placement / comparability for your system.