Which of the above three would you prefer new and how come?

I honestly don't think there's a wrong choice among those three. The UHX version of the 121 I don't think I've played yet, but the 121R has been one of my favorite new uprights for that price point (which was a lower one than the others mentioned here). The list prices on the Walter have increased a lot in the last decade - are the offered prices similar among these?

I like the Walter because it outperforms its size and it's a small, American, family-owned outfit. The looks can be a little polarizing, as the exterior design can look like a 1970s console in a way that doesn't appeal to me for some models. Warranty is transferrable. You have the choice of two different action suppliers.

I like the Kawai as being a well-balanced instrument at typically an attractive selling price/value. Other pluses include the composite action (so long as you like its performance), the transferrable warranty, and it's a well-known brand on the resale market.

I like the Ritmuller because the company (who produce a ton of pianos and have an enormous factory) seems to be trying really hard to break into higher-end production with certain product offerings, and are definitely among the more successful attempts coming from a Chinese factory. I might expect it will have a lower selling price than the others you're considering, as the wholesale price is likely lower and the brand is a less established in this market segment.

I have versions of each of these specific pianos listed in the Piano Buyer "Staff Picks" because I was favorably impressed with each.

I would prefer the Kawai as it is the only one that would be available for me to actually try in my area and I would never buy a piano without playing it. I have played a few used Ritmullers and was not impressed at all, but the ones I played were not representative of the current model you are interested in and which is (probably) a lot better.

If you do like the Kawai consider the 500 as well, this is more expensive of course but a really nice piano. And do pick the piano you like not what we would necessarily choose :-)