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Fine tuning can make a big difference but it's not absolutely necessary for producing a decent cup. Definitely would be finer grind size than for a french press, if it's too coarse it produces coffee that is under-extracted, sour, weak, etc. As I understand it, the grind size controls how quickly the water goes through the grounds and filter, so finer grind size means more extraction, coarser means less extraction. I like this because it means that if my first batch from a bag is not right I usually know whether I need to grind it finer or coarser to make the nex batch an improvement.
Filters come 100 in a box, I usually find them in stores for $8-10. They're high quality thick bonded paper made by Chemex. Figure using one per day equals $35ish per year. The other option is one of these puppies, which I've never used but know people who swear by them. I usually do 40g grounds to 700ml water, which leaves me about 560ml of coffee after extraction. Just enough for me and my wife in the morning.
I definitely prefer a Chemex to an AeroPress. I use mine with a kone filter. I used the hario kettle for a long time before upgrading to the variable temp. The catalyst was that my new place had a gas stove instead of an electric and I couldn't heat up the kettle on a gas stove without heating up the handle of the kettle as well.
Also, get a scale!
What do you mean by
> filters like those used for making espresso are fine
You can certainly get a stainless steel filters for drip coffee, like this one for chemex - or did you also include these in reusable filter screens you don't want?
To address your shape complaint - you can certainly perfect your technique to include almost all grounds in the brewing process using a cone. But to get a more even extraction, many cafes I know opt for Kalita Wave, which has a flat bottom. I didn't find any stainless steel filters for Kalita though.
If you like the oils, a metal filter like this will do the job. Don't have to use paper filters.
I've been eyeing the Kone for a while but I typically stay away from metal filters. I love the clean cup a paper filter produces but have had some excellent brews with the Kone v3.
I've also been wanting a pair of the notNeutral LINO mugs. Hopefully one or both go on sale Prime Day.
You could get an Able Cone ([link]). It will allow more oils to come through, and it's completely reusable.