2nd the burr grinder, because it is consistent unlike a blade grinder which spins the bean around like mad with inconsistent grain sizes.
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For coffee stay away from the supermarket beans, they have been in storage for an age and will have lost a lot of the natural oils in the bean.
Go for an independent roaster who will ship in relatively small batches 3 days after a roast so the bean is de gassed but fresh to grind.
I have used happy donkey for the last 3 years and they are very good, but there are others.
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Keep your beans in the freezer until you need them and aim to use your order of beans in a month, so you always get the benefit.
As for your stove top, keep it clean, fill the basket with an even grind of fresh ground and away you go.
Play around with the grind size and you can perfect.
The best advise with a stove top is don't let it over boil/heat