Bitcoin Core would definitely be the one with the most features and have no privacy compromises when you are talking about having a wallet. Bitcoin Core allows users to transmit transactions offline by offering the feature to sign transactions offline in the console. That being said, it isn't easy to create offline transactions and sign them.

Armory is the solution to this. Armory basically relies on Bitcoind, similar to Bitcoin Core, to synchronize with the network and make transactions. This is ideally a great setup to use.

However, you can also use Electrum and they also have the feature to create a raw unsigned transaction on the online computer sign it on an offline computer. Electrum is more lightweight but it does not offer great privacy nor wallet file security.*

*It is definitely strong but when comparing with Bitcoin Core: https://imgur.com/b59utxl