Look for moves that have some aerial properties or ones that crush lows to deal with the wake-up kicks. Incidentally, the ninjas have the best set of tools for dealing with wake-up kicks. Hayate's 9KKK for example, is great for dealing with those wake up kicks.
There are some characters that don't really have an answer to them, though. I don't think Kokoro has one.
Generally, you don't want to spam strings. Most of them are throw-punishable and nearly all of them are hold-able on hit. Some characters don't really have a choice in the matter and those that don't, usually have a few strings that are natural combos on counter hit. For example, Rig's PP2KK string is a natural combo to launcher on counter hit.
There are some strings that have a guaranteed unholdable number of hits; like Jann's PPP and Pai's PPP strings. Hayate's 6PK is also a natural string with a knocked blow to it too. Hitomi and Christie have a some of these too. One possibly easy way to find out if a move is unholdable is to look at them in practice mode and watch the combo counter. If the combo counter resets or doesn't count a certain it, it means that the hit is holdable or doesn't combo naturally. Hitomi's PPP string is a good example of this. Do note that some moves don't always follow this rule, Kokoro's 6PPP is not a natural combo on the first hit, but on the second and third hits it is.
