At that price range, stick with the plunger and buy a real grinder and use fresh beans.
A real grinder will run you about $100--either a manual (better quality but slow for more than 2 cups) or a Sunbean 0450 (a bit more that $100, but electric). Cheaper grinders than this are VERY UNLIKELY to produce the quality of grinding that is necessary for a decent cup of coffee. Especially avoid the whirling blade style which chop the beans into odd sized pieces and make good coffee all but impossible.
The strength depends on how many grounds you use, the bean, the roast, and the water temperature.