MCM curtains?  

I'm partial to floor-length pinch-pleated linen drapes that cover the top of the window frame. I also very much prefer the rod and any other hardware to be completely covered by the drapes when they're closed, so none of those big decorative rings! Ugh. They're ok for cafe curtains but not for drapes.
I have floor-to-ceiling sliding glass doors and I had to hang a sliding track rod thing from the ceiling for my drapes. IKEA actually makes a really nice one, very sleek and simple, and it works well and was pretty easy to install and can be configured a lot of different ways. It's called Kvartal. This photo is closest to what I did, but I posititioned the drapery hooks such that the top of the drapes falls just above the rod. I wanted only the drapes to be visible when they were closed.
I'll attach a photo I found online that is pretty much the vibe I have going. I wanted a cozy feel on winter nights, and I like the luxury of all that fabric hanging in perfect folds. There are lots of other looks that work too, though. I would just avoid super trendy stuff like those giant grommets at the top or the deep hems in a contrasting fabric. Also be careful of prints---make sure it's something you can live with for awhile if you're doing custom drapes because they are a big investment.
I think any style pleats are ok. I would definitely do pleats as opposed to gathered curtains, though. Gathered curtains seem to me like a better fit for overstuffed furniture and generally a softer look than mid-century modern.
Blinds are great too! I've actually had just blinds for many years. My faves were roman blinds that I made of cream linen, but I like anything with a clean, spare look.

The other thing I would caution against is not using enough fabric width-wise. You need a certain amount of fullness, otherwise drapes look cheap. I see this all the time with ready-made drapes. I guess people go by what it says on the package but that's just the minimum needed to cover the window. When these drapes are closed, the folds nearly disappear! I think the fabric width, measured flat, is supposed to be about 2 to 2.5 times the width of the area it is covering. You can always buy more panels, just don't try to skimp and get the minimum.
Of course that applies to any style of decor, not just MCM. Cheap curtains and drapes are a pet peeve of mine!

I agree with pretty much everything Spanky said.

Ah thanks guys, invaluable advice. So glad I recently stumbled upon this forum! Very much enjoying it.