Capresso
Infinity Conical Burr

Capresso
Capresso

Capresso

Oh! It's a capresso infinity burr grinder? Nothing exceptional but it gets the job done! Family members got it as a wedding gift years ago and never ended up using it and then offered it to me when I was newer on my coffee journey 😂
I’ve had a Capresso for 20 years and it should be in the price range if it’s available in Japan
Burr. It’s not very big
Neither of these are *enthusiast's* equipment, and won't do a stellar job of making coffee. I imagine you would get acceptable coffee from this setup, but it probably won't be as good as you were getting from the Chemex. You'll get what you pay for from the Cuisinart brewer: I would expect poor temperature control, and uneven wetting of the grounds. Hoffmann did [a video on cheap drip machines](https://www.youtube.com/watch?v=P-Ga8SRhRrE), what to expect, and potentially how to hack them, if you care for a perspective on this. The Braun Multiserve Plus is a drip machine that people on this sub like, currently on sale at Target for $130. I don't think you're going to do any better than your choice on a strict budget. The Capresso grinder is on par with the base Encore in my opinion. It's a decent choice, and a good match for either of these drip machines.
I started with a Behmor Brazen Plus 3.0 with a Capresso Infinity grinder. Moved on to a Moccamaster KGBT with a Baratza Encore grinder. Currently running a Breville Precision Brewer with a Fellow Ode 2 grinder. They are all great machines and brew very good cups of coffee. Behmor and Braville have customizable settings for water temp, bloom time etc. So to answer your question- I like the Behmor with the Baratza the MOST.
Ok the long game. Go for the $100 grinder like Capresso, which will get you espresso grind. Use it and make your parents their favorite drinks until they are hooked. Then ask for the nice expensive grinder.
This one. https://www.amazon.com/Capresso-560-04-Infinity-Conical-Grinder/dp/B001QTVXCS It does Turkish fine.
We have a Capresso Infinity Burr Grinder for 7-8 years now and it’s been great.
For $150 budget it's gonna be the Baratza Encore. Capresso Infinity is darn good for the money too. It's what I used before uograding to the Ode 2.
All of these will work for a Moka Pot. All of these will work with a less expensive espresso machine that brews pressurized like Stilosa. If you intend to eventually improve your espresso game by brewing non-pressurized, only P2 is (barely) capable of it. If it were me, I'd get Oxo, Bodum, or Capresso as they are well known good quality electric grinders, and plan to get a better grinder later should you get more serious about espresso.
Top recommendations from others in the same boat

Top pick
Multiple Brands - DF54 Series

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Multiple Brands - DF54 Series

Top pick
Baratza - Encore ESP

Top pick
Fellow - Ode Brew Grinder Gen 2 Series