You don't need a greenhouse for 98% of orchids. We do need to know your growning conditions though.

As smwboxer says, you need to know your growing conditions. Take notice of your windows. Does the light come in early in the morning? An east window. Does the light come in late afternoon? Possibly a west window. Does the light come in from late morning to early afternoon? A south window. No sun at all? A north window. Once you know what light you can offer an orchid, then you will be able to get a plant that has a good chance of surviving for you, as light is the most critical factor in growing an orchid.

Ok,I have 2 windows N and E,in one room, then bathroom has east and South, Front room hve several south and 1 west. lots of sun Is this any help Other room no room for plants

The light is not critical for growing an orchid but is critical on whether it will reflower again.

Phals and Paphs (lady slippers) are about the only orchids you can be sure will flower in your light conditions. Others may.

almost all orchids will do well in those conditions and re-flower if you put them outside during the months preceeding blooming season. Once the flower buds initiate they can come inside again to enjoy.

I'm in your zone and can bloom 'almost' every variety in south-west windows. East is also good. I do put my plants outside in summer, but there are many you can bloom from window light. Are your windows blocked by trees or overhangs? If not, you are good to go. Start shopping.

Jane

I will recommend an Oncidium. I am a phal killer myself. Killed 7 so far and I'm done with them.

Oncidiums are easy. Bright, indirect Sun and let them dry out nearly all the way between waterings. Feed regularly.

North window - Phals and paphs
East window - Phals, paphs, oncidium hybrids
South window - Catts, dends, etc...

A bathroom with both east & south windows sounds ideal for growing indoors. The bathroom has the added plus of additional humidity. All the plants smwboxer listed should do well in that room.

Enquire about an orchid society in your area. It's the best place to get inexpensive plants and LOTS of knowledge from others who grow in your local climate. Good luck and welcome to the forum.