Assuming that you’re looking for filter coffee, the Specialty Coffee Association and European Coffee Brewing Center both have certification programs for home coffee makers. None of these machines should be a barrier to getting a great cup of coffee, so you can comfortably focus on picking a machine based on price/aesthetic/convenience features from either of these lists. Even if you don’t want anything from these lists, looking at their guidelines will be helpful in knowing what to look for when selecting a machine. Naturally, the lists are nonexhaustive and only feature machines that have paid for the certification testing.
If you’re interested in manual brewers, some of the more accessible brewers would be the Clever Dripper, Ceado Hoop, Aeropress, or the Hario Switch. None of these brewers gets much benefit from using a gooseneck kettle, so you won’t need to jump too far down the rabbit hole.
You can try using this tool by Unspecialty to get an idea of the grind size/uniformity without buying any fancy equipment. As far as whether your grinder is up to snuff, I think how the coffee tastes to you is the best determinant. If it tastes good to you, it’s good coffee :)