Masdevallia is one of my favorite types of orchids! They have triangular flowers (the petals are tiny, so you just see the three sepals.) They need cool temperatures to do well, and like a lot of humidity, but are otherwise quite easy to grow. (But they have a reputation as being hard to grow from people who've ignored their temperature and humidity requirements.)
The Lycaste orchid genus, similarly to its relative Anguloa, likes intermediate-to-bright light, intermediate-to-cool temperatures, and high humidity. The flowers look rather different, though; they are more-or-less triangular in shape because the sepals point outward while the petals point forward. These orchids are very fun to grow, and will thrive if you get their care right.
Some orchids have water-storing organs, and some do not. If you have a type of orchid that has the ability to store water, such as cattleyas or oncidiums, you should allow the orchid to completely dry out before watering. If you have a type of orchid that does not have water-storing organs, such as phalaenopsis or paphiopedilums, you should water the orchid before it is entirely dry.
The Orchideae tribe is the largest tribe within the Orchidoideae subfamily, and contains a variety of flower forms. Flowers in this tribe dominate the orchid flora in the temperate Northern Hemisphere, though they can also be found in East Asia. These orchids usually have a three-lobed lip without a basal spur, prominent caudicles, and erect anthers.
Phragmipedium: Phragmipedium orchids are interesting in that they are one of the few orchids to produce vibrant flowers in an intermediate environment. You see, normally it is the extremes of climate that produce the most interesting colors. But this type of orchid is great for you if you have a temperate and mild climate but desire bright blossoms.