Get the Cuisinart. I got the earlier ICE-21 version and I'm very happy with it. BEWARE - the bowl works with a freezing gel that will get ruined if you heat up the bowl or even wash it with hot water. It won't freeze again afterwards. So always clean it with cold tap water and never leave it next to a heat source.
Cuisinart 1.5 Quart Frozen Yogurt ICE-21P1 Ice Cream Maker, Qt, White https://www.amazon.com/dp/B003KYSLMW/ref=cm_sw_r_cp_api_glt_fabc_TB6XV1PSACN81AVSVT1T
After buying this, we have never bought ice cream again. Really simple, easy to use, and SO yummy! :)
Since I'm a budget shopper, and had never owned an ice-cream machine before, I went and looked up all the different types. This one will make pretty much all you need it to (portion wise) and gets the job done just as good as any of the others I've seen on Amazon. If you're not going to be making ice cream all the time, it's relatively small, too, so you can put it away easily and store it.
My ice cream maker. There's a recent Serious Eats article hyping it up. I've had mine for about 5 years and wish I bought it way before that. It's the best thing ever ;)
I'm actually working on a blog about this so here goes.
What separates ice cream from a block of frozen milk and cream is the lack of ice crystals (I'm over simplifying, there's also air and other factors).
So when making ice cream you want to cool the mixture in such a way to minimize ice crystals.
The most common way to do this at home is by using a device like this one (https://www.amazon.com/Cuisinart-ICE-21-Quart-Frozen-Yogurt-Ice/dp/B003KYSLMW/s) which has a bowl you freeze 24 hours before hand in the freezer and then pour your ice cream mixture. As it rotates, it freezes and agitates the mixture (to inject air and minimize ice crystals). You get a soft serve like ice cream in about 30 mins and then put it in the freezer to harden.
More expensive machines have a built-in compressor that cools the bowl actively so you don't need to freeze it before hand but cost a couple hundred dollars (https://www.amazon.com/Cuisinart-ICE-100-Compressor-Cream-Gelato/dp/B006UKLUFS).
BTW I'm not endorsing any of the machines in this reply just linking to these devices as examples.
There are some other ways to do this without any fancy equipment. You can put the mixture in the freezer and then just stir it yourself every 15-30 mins until it hardens. Or there's the "bag in bag" method, where you just use two ziploc bags (the outer one filled with ice and the inner one with your ice mixture).
Finally there's a whole different approach that gets rid of the ice crystal by pulverizing them. The most common way to do this is to use a blender. Combine some ice and your mixture into a powerful blender to create ice cream (it will be like soft serve or a really stiff smoothie). Another way to do this is using the Ninja Creami or Pacojet, which takes frozen block of milk and cream and pulverizes the heck of it (and injects air) to create ice cream.
All of the above methods should be google-able. Not sure how much you want to spend but if you're just getting into ice cream in general the best place to start would be conventional cuisinart rotating freezer bowl I mentioned at the start. It's cheap and common and easy to find recipes. My personal favorite these days though is the Creami because it seems to be very forgiving if you're making lower calorie or ice creams with non-standard ingredients.
Mix: https://www.amazon.com/Dole-Soft-Serve-Pineapple-Pound/dp/B01666JBFG/
The ice cream maker I personally use that works great: https://www.amazon.com/Cuisinart-ICE-21PK-Frozen-Yogurt-Sorbet/dp/B003KYSLMW?ref_=ast_slp_dp&th=1
The method I tend to follow: https://youtu.be/ZLhjuWRVBuw?t=142