Lufthansa is Germany's flag carrier. They have a very good reputation for safety, but their service leaves much to be desired both in the air and on the ground. Most flyers complain about both quantity and quality of the meals in Economy and about the apparent rudeness of many longhaul flight crews. Seat pitch is way below average and the seat width is also tight on the A330s and A340s (and not much better on the 747s). If you have a choice to fly on United or other Star Alliance partners, I would strongly recommend that. Lufthansa seems to mainly care about their Business passengers.
Lufthansa does not offer in-seat video in Economy on any of their aircraft, not even the brand new A340-600. There are only overhead monitors or central screens, depending on the equipment used.
On German domestic routes, there is no meal service in Economy and on flights with short durations, there isn't even beverage service. Lufthansa does however provide free coffee and a choice of teas along with newspapers at many (not all) departure gates.
There is no charge for advance seat reservation, but it is only available on intercontinental routes and select European sectors, but never on German domestic segments.