I think some of the best that I saw are these

• Hungry Game (Tough one)

• By Elevator or Stairs? (Very Fun)

• Planar Relection, Unsolvable :(

• Sending a Sequence Over the Network (Very Fun)

• Three Strings

• Linova and Kingdom (Graph)

• Mortal Combat Tower (Fun)

• Hits Difference (Hard DP, or EZ DP with an observation)

use death spell

this is going to sound weird but you need to just say it, just say to your self, lets say i knew the answer for all _______, could i then know the answer to the problem, can i transition in a reasonable time? usually its pretty obvious what types of things you might want to know, then its just a matter of picking one that has good complexity and transitions. You need to do some more problems(as do we all) but lowkey at your current level, the hardest part should be realizing it is dp, rather than actually finding the right dp or the right transitions, so just add it to your problem solving system i.e don't forget to stop and say "if someone told me this was dp, how would I solve it?"

Here are two nice problems:

https://mirror.codeforces.com/contest/2031/problem/D — this one makes dp feel almost like magic, just trust the logic

https://mirror.codeforces.com/contest/2037/problem/G — need a tad of combinatorics knowledge