"Will it lower my water pressure?" Maybe a tiny bit, especially with cheap filters. Get a filter rated for higher flow (like 2.5 gallons per minute). Your shampoo won’t notice.
"Do I need one if I have well water?" Depends. Well water can have bacteria, sediment, or iron. You might need a sediment filter first, then a carbon one. Don’t just wing it—test your water.
"Is it worth it for a rental?" Absolutely. Showerhead filters are removable. Take it with you when you move. Landlords hate this one weird trick—just kidding, they don’t care.