Kyle if you want iced coffee you will be far better off to brew in a toddy brewer, cold French press isn't that clean and I feel like the end product can often be more bitter than it should be.
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I have a couple hand grinders myself, nothing at all wrong with using them. Despite also having 2k in electric grinders, I enjoy using mine frequently, especially when doing the more manual process of pour-over.
For beans one needs to realize that in cold brew more of the nutty and earthy tones come forward and that you lose all of the floral and mostly all of the fruitiness. So as David said, your bean choice should reflect this, and lesser coffees will taste better as an iced brew than they would have hot. Personally I still believe in drinking single origin iced coffee though, just don't spend $25/lb on a Guat because it exhibits a beautiful honeysuckle note. I like to look for things with black fruit and chocolate as descriptors, as well as good earthiness. Also, while I don't mind spending $25+/lb on something I will vac-pot, I try to keep an iced candidate around 15-18. Some suggestions for origins would be Brazil, Nicaragua, Papa New Guinea, Bali, Ethiopia.
If you really get into it you can get an ice drip brewer one day, that is actually next on my coffee item list.
It produces an end product that is oddly rich and unctuous, picture a cocktail of Frangelico and Kahlua on ice. I find 4oz to be an ample serving on ice, and it also dilutes well for a daily type drink.
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I hope some of this info is useful for you. Happy brewing.