I use electrum for transactions and store some coin in paper wallets, (the address next to my avatar is a paper wallet containing most of my coin).
I generate the paper wallets on a Linux cold boot using
bitcoinpaperwallet.com.
I don't have much coin yet (11.3565m
BTC to be exact), I hope to earn some this spring if I am not too busy.
I am running Core 0.13.0, it did not synch yet (if it is not open but visible in dock, is it still processing transactions?), and I don't plan to use wallet anyway, I am just running to support the network.
A Trezor would be great, but it would cost about ten times more
BTC than I have.
I use blockchain.info to look up transactions and addresses, and bitcointalk.org for discussion with other bitcoiners.
I think I already started a thread very similar to this one, and found that, unfortunately, web wallets are very popular.