Tickets for visiting the Berchtesgaden Salt Mine are available online. There is no discount for purchasing tickets in advance. But you can choose the time to visit, and you don't have to wait at the ticket counter when you arrive if you purchase in advance.
Summer can be very crowded in Berchtesgaden, but it is when the weather is the most beautiful. Lines to catch the boats can become very long in the afternoon.
Visit the salt mine on the first tour in the morning (9 a.m. in the summer) so that you can get to the boat dock before the afternoon rush. If possible, take a boat to St. Bartholomä before 11 a.m.
Late spring, summer and early fall are the best times to visit Lake Königssee. The boat tours are open year round unless the lake is frozen, but the hours are cut much shorter in the winter. The Berchtesgaden Salt Mine is also open year round with slightly shorter hours in the winter.
Both the salt mine and the boat tour offer family passes which will be a better deal if you have several paying children joining you. I would recommend packing a picnic lunch if you don't want to have lunch in Königssee or at the biergarten near St. Bartholomä.