Could you please advise us about which wallets are SegWit (to take advantage of the lower fees), and which you recommend, and why?
Sure thing. The wallets which I know about include the following:
Hardware wallets: Trezor & Ledger Nano S
Desktop wallets: Electrum and Armory (and Core 0.16 when it’s released, should be soon)
iOS wallets: Edge, GreenAddress & BitWallet
Android wallets: Samourai, GreenBits, Electrum
The one I’d recommend really depends on your system. Either hardware wallet is really good, as it can be used in combination with some of the other types and is a great way to keep your bitcoins as safely as possible without sacrificing much convenience.
Note that Electrum’s native support for bech32 addresses is not compatible with a lot of other wallets at this time. It’s better to figure out how to use P2SH addresses with Electrum instead (they have a guide to this online).
Oh yes, and SegWitAddress.org for paper wallets.