This all greatly depends on which character you're using down throw on as different things happen to different opponents when they are thrown. Keep in mind I'm just giving you a general guideline here, there are WAY more in-depth things out there.
Fox/Falcon/C. Falcon - These three characters fall faster than any other character in the game. When dthrow is used on them it is near-impossible to get an instant follow up with a move. What you should be doing is waiting until they hit the ground after the throw and reacting to which way they tech (towards you, away, or in place) or if they tech at all. This is called tech chasing. If you react quick enough you can follow up with another grab and start the tech chase all over again. If they don't tech they are open to jab->regrab, usmash, dsmash, or you can sheild their get up attack/react to their roll/neutral getup and try for another grab. These all usually work as long as you time them right.
Marth - IIRC there is a fantastic guide on dthrow specifically against Marth written by Druggedfox if you can find it. Marth is more floaty than the three characters above so he gets popped up after down throw. A good (albeit hated) follow up after throwing Marth at lower percents is to react to his DI then go for a regrab before he hits the ground or is able to double jump away. Some other options for if his DI puts him closer to Sheik is regrab, utilt, uair, and usmash. If Marth DIs away you can regrab, ftilt, or fair. Keep in mind the chaingrab doesn't work forever.
Sheik - This will be a lot similar to Marth, only Sheik doesn't get sent quite as high as Marth does. This will be another situation where you should be reacting to your opponent's DI. If they go away you're almost guaranteed an ftilt, if they go in you can use a number of moves but I like dsmash at lower percents. Sheik is also very easy to chaingrab if you react properly so if you're into that go for it.
Jigglypuff - I won't lie I'm kind of bad at this matchup but the gist of it is if they DI away, fair. If they DI in, uair.
Peach - Honestly the hardest part about this is getting the actual grab but I won't get into that. At lower percents if peach DIs away you can get a regrab. If she DIs in you can usmash. At higher percents you can fair or uair again depending on the DI.
I feel like I'm forgetting about a few higher tier characters but oh well. The main thing you should take away from this is that there is no "correct" move to use every time. You have to react to what your opponent is doing and choose your moves accordingly. I also strongly urge you to seek out other guides because they go way more in depth than I just did.
Good luck!