You can use any washer with the kitchen sink, with buying just a few parts to adapt to sink use.
I've had a couple of portable washers. One was a Whirlpool with wheels and one was a Haier. The Haier didn't come with wheels, but through the magic of the internet I was able to learn that I should buy wheels for it at Lowes that screwed into holes in the bottom and not the Haier wheel set. It worked great, but if the machine wasn't completely level, the machine would not work right or would not operate at all. Some people put the Haier washers without wheels on dollies.
A regular washer will also work, as long as you have the space for it. You can buy a Y-shaped hose part that attaches to both the cold and hot intake rings, leaving a single attachment hose for screwing into the faucet. The only issue with a stationary setup is that you need hoses for intake and output that are long enough to reach the sink, and dealing with the long hoses in the kitchen might be a challenge.
There are many Youtube videos on all the various solutions and how to do them, and what parts you need to buy.
My only caution with the portable washers is that many of them are so small that you will end up doing many loads and will tie up your sink for a long time. I recommend buying the largest capacity you can find that fits your space.