I am a long-time SD resident and have boated extensively on all the Missouri River lakes for many years in my R-21 Classic and R25sc.
You can anchor pretty much anywhere on the Missouri River lakes...except where buoyed in proximity to the dams and powerhouse structures, swim areas and that sort of thing. The Corps owns the vast majority of adjoining land, so there are no private landowner restrictions.
Navionics has very good bathymetric coverage. The lakes do indeed go up and down based on power-generation water discharges from the dams so you need to compare chart datum to the current water levels, which are published on the Corps website for each reservoir.
All the lakes have many high-quality Corps-style boat ramps. Marinas are few and far between. Lewis & Clark (furthest downstream), has two. Francis Case (next upstream) has four with about 150 miles from the downstream end to the upstream end. Lake Sharpe (next upstream) has one marina in Pierre but it is often accessible only by shallow draft craft. Oahe extends all the way to Bismarck, ND and has two "real" marinas toward the south end. There are a few other fishing-boat marinas, but not what you would consider full-service. There are really only four "full-service" marinas: L&C and Weigand on L&C, Cedar Shores on Francis Case, and Spring Creek on Oahe.
Gasoline is available at all the marinas (usually), but diesel is only available at the L&C Marina near Yankton. There is at least one pump-out available each on L&C, Francis Case and Oahe (when the equipment is working). RV pump-outs are abundant at the State and Corps parks - and you will obviously be trailering. Off-road (dyed - no road tax) diesel is widely available at truck stops for about 50 cents less per gallon.
In many (most?) areas, this is wilderness boating. There is no BoatUS or SeaTow. You might be a long way from any help, but you will have the opportunity for some real solitude. Anchoring will be mostly good mud. On most of the lakes, there is world-class walleye fishing.
Hope this helps.