What kind of Throw things should I be doing on Sonic/Peach/Zelda/Bowser?
While it depends a lot on playstyle, a good mix of guaranteed strategies and mix-ups are a good plan. Have a default combo game of cargo uthrow uair and be wary of platforms. DK has a smiilar platform game to Falcon and can do plenty of follow-ups with his dair of uair provided that you are patient and don't try to hit them before they hit the ground.
That said, and against floatier characters (anyone who isn't a spacie pretty much), you can pull off forward/back cargo throws on which your foe DIs up, the opposite direction, or not at all, from which point you can combo with nair and a handful of other moves. At first, though, it's best to keep it simple with uairs and nairs until you figure out the flow of his moveset.
DK is a character with a ton of multilateral combo potential in that he doesn't just need to uair constantly like he did in Melee. Exanple: Cargo fthrow -> low nair -> utiltx2 -> uair up platforms -> dair onto platform -> reverse dair/falling uair after tech->usmash/fair/GP. This is more or less a guaranteed death combo for Sonic and Bowser. If, however, the foe is constantly trying to DI offstage, nair is the best option, because it forces them to choose between flying offstage and potentially dying outright, or suffering bad combo DI and getting killed with a GP or fair. Here's another example that works on most characters:
Cargo uthrow ->autocancel uairx2 ->nair (until sufficient) ->GP/fair. DK's nair sets up for his Giant Punch so well that opponents are often scared of it and will DI way offstage which is a win/win situation for DK. GP is the optimal combo finisher in almost every situation, but where fair will do, GP can be saved for later to get earlier kills on another stock.
As far as super-floaties go, they kind of expose DK. Most of them can blast out of seemingly every grab combo you can get on them so it's best to go for lots of pummels and uairs for guaranteed damage. Cargo uthrow (from the ground) leads to uair kills on floaties a lot of the time so be sure not to let Peach take you to Dreamland or GHZ where she can live for hours while you get edgeguarded and camped out repeatedly.
Just remember that after your opponent has begun to DI a certain way out of cargo uthrow, a f/bthrow to the center of the stage almost guarantees the amount of damage it will take to kill with GP. Guarantees are nice and all but the occasional 0-death comes much more easily with good mix-ups.
Bonus notes:
Jab Jab extends a lot of combos in a pinch
Turn-around utilt hits a surprising distance behind him and the opponent can't reliably DI far enough away to avoid a follow through in many circumstances
DK can combo far offstage with dash attack; cargo u/bthrow lead(s) into it all the time. You can completely bone so many characters at low percentages and the heavier foes can die to a fair. Keep in mind that it gives DK a slight boost in mobility as well. This will basically always give you an outright kill on small stages like Yoshi's or WW.
GP kills super early and it doesn't need to be charged all the way to kill.
DK can combo down as well as up and forward/back. Cargo throws lead to dair on Sheiks and Marths which help keep them well within your grasp.