hi Marleneann,
i'll start this off for you even though my knowledge of these plants is really very limited.
Epiphyllums i like but sad to say i do not have very many.
off the top off my head i have:
E. anguliger - small white and yellow fl.
E.ackermannii - red fl, pictured below
E. crenatum (i think) - big white fl.
E. oxygona (the best!!) - pure white, highly scented, only lasts one night, shrivelled by following morning.
E. phyllanthoides - pink fl
E. massive orange fl hybrid (pictured below)
unknown red (pictured below)
unknown white
unknown yellow
I want Epiphyllum chrysocardium.
its like a giant Epi anguliger.
and really amazing.
another cool one i've seen is cv. 'Clown'.
Epis are great plants
The flowers are just incredible
and the fruit taste good too.
Selenicereus are also well worth growing.
and try hylocereus also
and Disocactus
Rhipsalis too. flowers are small but they bear hundreds of them at once.
all these epiphytes enjoy the same sort of conditions.
Not to get this too far OT,
Epis can, despite their apparently different preferred growing conditions,
even be used as grafting stocks for small choice desert cacti species.
i remember seeing an excellent Loph graft onto an epi on the internet.
sure they are not commonly used
but i still think they have potential for this purpose.
particularly in highly humid areas
even if they are not as good as the more common Hylocereus and Selenicereus SP
also i've been thinking about Rhipsalis as stocks;
i think HN was talking about this at one point?
here are some pics i dug up from last season for your enjoyment.
(its too early here for blooms now).
unknown red:

Epiphyllum ackermannii

E. massive orange fl hybrid:

sorry i do not have hybrid names for them. they were purchased unlabelled.
Pure species Epiphyllum can be hard to get, possibly due in the extensive hybrdisation with the literally hundreds (thousands?) of hybrid cultivars.
i don't grow many because they need higher humidity, shade and more water & ferts than most of the desert cacti which i grow. plus they take up room. so i don't grow them in greenhouse. they grow well under cover in hanging baskets.
actually i think my main limiting factor is that they just aren't cactus enough (

). almost spineless and too lush lol.
oh and the very limited flowering season and the plants are not (imo) exceptionally attractive when not in bloom.
i think gilligan here also grows a few epis, and from memory did some hybridising too(sic).