I've been using it for years (the same filter, actually), it's excellent, and lets you brew by-the-cup easily. French press pots are a PITA to clean. The mesh is way finer than even the finest grind, though a blade-based grinder will make more dust than a burr-grinder.
Make sure you get a decent filter, though. Many of them aren't super-fine. I personally got mine from SpecialTeas for less than I see in stores, and they've got good tea too: http://www.specialteas.com/Tea-Preparation/Permanent-Tea-Fil...