We also have a slider and a small kitchen window over the sink and get intense afternoon sun. I have used insulated curtains for years now and love them. They keep the heat out in the summer and the cold out in the winter. When I bought my new curtains for the slider, after I remodeled, I bought an extra set and had them hemmed to fit the small window. I just pull them closed on super sunny days. No more mini blind.

Curtains would block the sides of the windows a bit even when open. Since your sink is to be centered on the stationary side, I would be concerned that curtains might interfere with seeing out. Maybe just blinds? Or blinds with a fabric valance if you want some softness or color or pattern there.

What's the overall style of your kitchen?

How far from the window will the upper cabinets be? If you choose curtains, you could have a wider rod so that when open, the curtains clear the window.

Have you looked into solar roller shades? They block the UV/intense sun, but still let you see outside.

I vote for the solar shades. They would look nice with the vertical blinds and when not in use disappear when rolled up.

The cabinets will be fairly close to the sides of the window. I'm leaning more toward blinds as light can be filtered better than with curtains. I hadn't looked into roller shades - I didn't know you could see out.
With either blinds or shades, should I use two, lining up the split between the window sections? Two shades makes sense, but aesthetically, I'm struggling with whether it might look odd.
The overall look is "transitional." Not exactly sure what that is, but it's the style that seems to come up with various surveys :). The walls will be a light tan/beige; the windows will have white 2" or 2.5" flat trim. Light wood floor, medium wood Shaker-style cabinets and white-ish granite countertops, still waffling on backsplash ideas - goes well with the mid-60's boxy split-level house.
Thanks for the suggestions so far!

Here's an idea of what solar shades would look like

http://accentblindsandshutters.com/shades/solar-shades

http://www.sears.ca/product/wholehome-md-ultra-sunshield-cut-to-fit-roller-shade/624-55365-55365

https://www.windowcoverings.com/?blindsshuttersandmore/roller-shades/solarscreen-shades-decorative-fabrics-4-openness.html

I think I personally would just do one - air flow is still possible even with it pulled down.

Really hot and sunny? I would bite the bullet and get room darkening cellular as they really block heat and sun.

I've never spent time with solar shades though I have lived with 3M films, so my question is this: when you are at the sink when the sun is descending, so you are fully facing the sun, do solar shades block the sun glare enough so you can work and it's not in your eyes?

Thinking through this a bit more, solar shades would be a great option if we experienced consistent sun. However, we only have direct sun through that window for about 3 hrs in mid to late afternoon, and then there are plenty of cloudy days throughout the year that make it less intense. Thankfully the Pacific NW isn't super hot or humid in the summer.
Usually anyway - tomorrow we're hitting 100 :).
So that's bringing us back to blinds as probably the best option - they can filter enough light, but wouldn't block the sides or top of the window.
The next question is one set for each side, or one big one for the whole window . . . ?

Haven't installed my solar shades yet so I can't say totally. I will tell you that the window where we have the sun setting in our eyes while we watch tv is way beyond solar shade - we have a curtain there. And solar shades don't give privacy at night. But they are good for when you really wish the window could be open b/c you have a gorgeous view, but need to keep out some heat and glare.

Mama Rachel - Yes this is a Milgard window :). It's 62" wide x 44" high, and the casement is 18." The size was custom, but from the way the contractor talked, these custom sizes are easy to do and not much, if any, more expensive than standard sizes.

stephanj says the solars do not give privacy at night. Mama Rachel says no one can see in . . . which is it? Or does it vary by brand?

We need a third opinion lol...

We had solar shades in our west facing loft and they provide no privacy at night. They do significantly cut down on the heat and glare making it possible to look out the window. We did it because we did not want to have anything blocking the view. In my opinion insulated blinds would have worked better but we did not want to live in a cave every afternoon.

I loved seeing your kitchen window. I did the same kind of window (almost exactly) so I could enjoy the view from the sink without an obstruction/divider, yet still open the side window for fresh air (and mine is narrow enough I could accidentally leave it open and no one can crawl through it). I put an exterior solar shade on a west facing window, with a remote to lower it because I didn't want it mounted inside the house. You can look out without the sun bothering your eyes; you can see out very well. There is no night time privacy. I ordered it from Costco and really love it.

I like Crl's idea...blinds with a valance :)

These look like they would work out well.

http://www.jcpenney.com/jcpenney-home-custom-shadow-rolling-shade/prod.jump?ppId=pp5004310059&catId=cat1003990022&deptId=dept20022800026&&_dyncharset=UTF-8&colorizedImg=DP1008201417071993M.tif

Thank you for the window info. I like it so much I might ditch an upper. Wow!