Best On-Chain Analysis?

I am trying to find out what is the best way to do analysis for past transactions that can be seen on-chain.

What is the best way to go about this?

Specifically, I am trying to identify the receiving party of a transaction to verify the claims made by the sender regarding what the transaction was for.

There are potentially a few scenarios that may have occurred, such as, if the receiving party has had their coins seized by law enforcement, is this easily identifiable somewhere?

Or the sender performed multiple transactions to potentially multiple addresses but all of those addresses are affiliated or were involved in an operation which was later found to be something like a marketplace known for selling contraband that has since been shut down by authorities, can these transactions/networks of wallets be searched or otherwise correlated with other information that I may have off-chain?