I recommend using
Bitcoin Core as your hot wallet and your Ledger Nano S as your cold wallet.
Here are five reasons why. Most importantly, using a full node as your hot wallet
contributes to Bitcoin's economic strength.
If you are unable or unwilling to store the entire Bitcoin blockchain, you may run Bitcoin Core with pruning enabled, using the
-prune= command-line argument. (The Ledger Live app may also not work properly with payments from coinbase transactions, which is how this pool pays its miners. There is currently no documentation from Ledger regarding this.)
It's worth noting you can substantially decrease your bandwidth requirements with bitcoin core by enabling the blocksonly mode. You will have the same level of security, can still send transactions, the only difference to you is that transactions will need one confirm before they even show up in your wallet. This is actually more secure anyway, but a little disconcerting if someone has just sent you some coin as you can't see it till the next block passes. You are not supporting the network as much as a full node, but you are still helping slightly.
Note that no light wallet will ever be as secure as a full blockchain based one, but another alternative for a secure low bandwidth light wallet is still greenbits on android or greenaddress on iphone - they have a web interface you can use on PC as well if need be (
http://greenaddress.it ). These are not as flash as some of the newer wallets but get the job done and have all their code open and auditable.