You have a variety of choices depending on what your opponent will try to do after they are knocked down. Understand that what move they are knocked down by (or launched by) determines how much time you have before you can attack your opponent before they can stand up, as well as determining how far away your opponent lands.
The three main things your opponent will do in this situation are as follows: stand and guard, lie there, and roll away.
- Counters "stand and guard":
Throws (duckable)
Safe moves with heavy guard damage such as 1B, 1A, 1K K, 4A+B, 4B (B), 3B+K, FC3B, and 6B+K
Low attacks such as 2K, iWR A+B, 2A+B series (can cancel into BT 2K/Throw/BT B+K), and 22K (plus 22kA series)
Guard breaking moves such as FC3bB, 2B+K, 44aB (and similar), 66B series, and 44K
Frame trapping moves such as 4A, 4K, and WR K (all -2 on block)
- Counters "lie there":
Ground hitting moves such as 33B B (unsafe at close range on block), FC3B, 2K, 1B, FC2A+B (unsafe), 66K and 44K
Moving to an advantageous position by sidestepping or moving forward for a better/scarier mixup on wakeup
Moves with really long active frames like44[A], 33B B, and 4B B can partially whiff but still make contact with your opponent. This is not ideal, but these moves require that your opponent firmly commit to staying flat on the floor.
- Counters "roll away":
Ground hitting moves with good tracking/relatively fast startup such as 1B, FC3B, 3B, 2K, 66K, 33B B(whiffs if you don't delay it properly)
Moving parallel to your opponent to prevent them from changing their position relative to the wall/edge
2B+K (sets up big damage with AA BE, builds meter on ground hit, and sets up a mixup on close-up block)
Moves that fall into more than one category are marked by color as follows:
Counters Blue and Red = Purple
Counters Red and Yellow = Orange
Counters Yellow and Blue = Green
Potentially counters all three: Bolded Teal
Bear in mind that your opponent can also attack on wakeup, but this is only a good option if their move is either faster than yours, or if it has some kind of defensive option built in such as auto guard impact, tech crouch, or even tech step. Smart opponents usually won't use this much, provided that you are careful enough to avoid using really slow moves over and over.
(TLDR) Stick to purple, orange, green, and teal moves to cover the most options simultaneously. My top 3 recommendations overall are
FC3B, 2K, and 33B B. Use FC3B and 2K when you think they'll block, and use 33B B to punish them if they stay down. Sprinkle in a few throws and you're all set.
To get you started, use 1B after a launcher (3B, 22B, FC3B), then use the above mixup. Since 1B puts you into a full crouch, using FC2K and FC3B is easy. To throw, just buffer 66 in there after 1B ends, then throw as soon as you see them rising off the ground.
Hope this is helpful.