What kind of coffee do you make at home that is strong?
Columbian coffee is strong, depending how many scopes you put in to the amount of water. Now there are some people that like it so strong that the spoon stands straight up and wants to take
a walk out out of the cup.
All these answers are only part right, but you didn't ask it right either.
Strong tasting or strong caffeine content.
Stronger tasting coffee will have less caffeine than a lighter roast.
So if you want stronger taste, go for a French roast (it will have less Caffeine though)
Stronger caffeine, go for a medium roast or a Breakfast Blend (not as strong a taste, but a better "wake up")
Roasting leeches caffeine and oils from the bean, so the darker the roast, thes less caffeine.
3 yrs as a Starbucks Manager
Strength is a matter of how many beans per cup of water, mostly. Some coffee makers tend to brew stronger stuff, like the stove top espresso makers. And grinding the beans finer will make it stronger. But pulverizing them too much isn't good for the taste.
Taste relates to what beans you buy, and grinding your own will make it fresher. Quality goes up with costs, but there are deals on good beans, like bulk buying or finding an off brand that tastes good.
You need to get fresh coffee beans first, grind them up and then get a stove-top coffee kettle. Works great and is strong.