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My bad, i wasn't aware that a wallet that doesn't relay transaction or having it behind a firewall that refuse incoming connection could be considered a node or a full node. After all you can use them offline and in no way they could be acting as a node while offline.
Core relays and verifies transactions according to the "is Standard" rules. Even if you refuse incoming connections you still have 8 outgoing connections to the network. You still get incomming traffic, you just dont allow others to initiate the connection. A full node behind a firewall with limit to 8 connections is certainly less helpful to the network than a fullblown dedicated server that can handle >100 connections, but its still a full node. This is even true for pruned nodes even though they are less helpfull as they no longer relay blocks. They still however relay transactions.
Offline however I would agree that you should not call core a full node, because without a connection to other nodes there is nothing to verify or relay.
I dont like multibit, its design is ugly and its hard to use for first time users. I had easier time to use Armory on first use than multibit, but they claim that their design is simple.
I think mSIGNA is superior to multibit, and in some cases even to Armory.
mSIGNA is very odd IMHO. I found it overly complicated, you need a full node (as in you need an IP) that it can connect to and you cant sign messages with it. Its certainly a very powerful wallet, but I dont think it should be recommended as first wallet to anyone.
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1. Bitcoin-Qt: Bitcoin-Qt also knows as Bitcoin Core is the original bitcoin wallet. This is a full-node wallet, which
downloads the full blockchain which is about ~30Gb. Only use it if you have a lot of free disk space.
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Correction for the OP: core needs ~50Gb currently on Windows (excluding wallet file). Bc.i lists it with 45Gb ->
https://blockchain.info/charts/blocks-size