This really depends on your threat model. Depending on what information you're protecting (and who you're protecting it against), Lastpass is just fine. With a different model, you can use KeePass on a standalone, airgapped, encrypted Unix machine and pray to God your info is safe.
Lastpass is fine for your recipe web site account. To some extent, they're excellent for even other personal consumer account protection. Remember, Lastpass uses "zero-knowledge" encryption, so by design, the fact that they host your password data is no different from one of the alternatives you mentioned....
Which is KeePass + your cloud service account. I really have no idea what advantage you gain by doing this instead of just using Lastpass anyway. Seriously, what's the difference?
KeePass stored on your local machine will be about as secure as your machine (or any local media the password database is stored) is.
The best way to approach the problem is to do your own personal risk management analysis. That just means... figure out what's most critical to protect. Figure out whats less important, and finally what's least important. Consider what/who you're protecting that data against, and then plan your defense strategy accordingly.
It really should (and does) depend on all these factors combined. There is no one perfect answer.