Stainless is probably the best match, and the most "neutral". Your sink is stainless. It will look fine! Plus it will be the easiest to match when you need to update your other appliances one day. I have black appliances in my kitchen and have been replacing them one at a with stainless. Mixing looks perfectly fine to me, since (like I mentioned above), stainless is neutral.

I don't like the white DW in this kitchen -- even though it's a new appliance, it somehow looks dated in this context. (And it might be a different shade of white from your other appliances.)

Black stainless looks nice in this mockup, but be warned: that finish is achieved with a transparent film over stainless, meaning scratches will be very noticeable. IDK if they've made improvements over the years to make this stuff more scratch resistant, but it's something to consider (and of course toughness of the finish will vary by brand).

Just my own preference but I'd get on that stainless train, for sure. Stainless has been around for a long time and I'm confident that will continue. The stainless looks best with your cabinets since it's neutral. The white looks too bright/stark, and the black just too dark. Also, black appliances can often look too dark to me and become black holes. If it's any help, I spend less time cleaning my stainless appliances than I did with white ones in a previous home.

Oh also -- mockups help, but note that the lighting and color tone is off. It appears very bright compared to the other stuff in your kitchen (look at your sink). It's so bright that might be throwing you for a loop, but it won't look like that in real life.

A stainless DW in that spot, under your lighting, will look a little closer to this:

Another vote for stainless and also choose stainless when you upgrade your other appliances. Stainless is not a trend.

I'd go stainless, especially since the dishwasher is right next to your ovens - whites are hard to match! I wouldn't worry about stainless going out of style anytime soon.

White works with miss matched items. Looks cleaner than black. But we ended up with a stainless steel dishwasher, due to availability. Haven't looked back on the choice, after 2 months now. Had planned on removing the stainless door panel and spraying it with VHT Black Tent wheel paint. Kind of like black chrome look. Though stainless acutely looks cleaner than white from water drips and touch marks. Most new dishwashers have a durable clear coat, which makes a quick wipe down a breeze.

See what's in stock- there's no point in waiting many months when you have a young family producing dirty dishes all day, every day. Either stainless or white Bosch dishwashers would be fine- don't turn down the white one if that's all they have, and the same for the stainless one.

Sooner or later, the fridge and ovens will need replacing. You can cross that bridge when you come to it.

I think a black stainless would look nic w/your other elements. It's not going anywhere. you can slowly upgrade to the same finish w/the other appliances go.

if you fridge is that ancient, check for deals on a new one. sometimes if you buy the package (stove too) you can get a better deal. and they have 0% financing for over a year. pretty good deal.

(I also need a new DW but need black. long lead times.)

some pics of similar cabs/counter w/diff finishes

here's a mix of black and SS. (I couldn't find any w/the white. the white would be the least fave)

we were in a similar situation when we bought our house (all the appliances were different in black or white and slowly dying) and our cabinets are a similar color but i have lighter counters. the first to be replaced was the fridge. i found stainless is the cheapest and has the largest selection - i would see white and black being upcharged several hundred dollars. I went with black because i still had some black appliances. now everything is black except the dishwasher (i wanted a specific model that wasnt available in black, but looks ok) and we changed all the cabinet handles to black, and painted the walls lighter. it looks so much better. But agree with others that with your black counters i would go stainless and update your knobs to match.

White would be my preference guven the other appluances you have. oh oh, and I confess to being so jealous of those vintage analog wall ovens on the pic you shared. sane goes fir the vintage fridge you described. Given how short lived most modern appliances are today, I eould hold onto those vintage appliances fir dear life.