1. A *client* and a *wallet* are one in the same,
There is a lot of slop in how these words ("client", "wallet") are used. This can lead to some confusion. Technically (as far as I'm concerned), something is only a "wallet" if it allows you control over private keys. As such, Coinbase is an "account" (like a bank account), and not a "wallet". A "client" on the other hand would be anything that connects to bitcoin peers and communicates on the bitcoin network. Many wallets are clients (such as Bitcoin-Qt), but there are wallets (such as paper wallets) that are not clients. It would also be possible to create a client (that simply acts as a relay) that isn't a wallet.
in that I can't use Coinbase as my client, but have Electrum as a wallet for the same address... I need to pick either/or, correct?
You can have a Coinbase account AND an Electrum wallet if you want. It is generally a really bad idea to try to share addresses between multiple controlling entities though. Each wallet or account that you use should have its own unique set of addresses. None of these "wallets" or "accounts" are really designed to synchronize between each other. So if you have an address in Electrum and you import that address into blockchain.info, you run a significant risk of creating a transaction in one that the other doesn't know about. This leads to lots of confusion and angst over lost bitcoins, double-spends, and invalid balances.
2. I have to choose one device to download the wallet to. Anyone who hacks, steals or otherwise has access to my device would then have access to my Bitcoins,
Yes. There are solutions that add inconvenience but which reduce this risk. One such solution is Armory. Encrypting your wallet with a password can help quite a bit, although it won't help if you end up with keylogging malware on the device that captures your password when you type it.
unless I take them off the device and put them in "cold storage" (which is the same thing as "paper wallet.)
Paper wallet is one form of "cold storage" You could also look into Electrum offline, and Armory.
3. Paper wallets/cold storage is only truly safe if every trace of "private keys" is wiped from the device they were originally created on, correct?
Correct. Anyone with access to the private key can ALWAYS spend/steal the bitcoins. Cold storage is just a way to significantly reduce the potential access to the private keys.
4. Best way to get my "feet wet" would be to choose a wallet and have someone send me a minimal fraction of Bitcoins, right?
I'd suggest purchasing an "educational quantity" of bitcoins. Something you can play around with and not get upset if you accidentally do something bad (like deleting a wallet, or posting a private key to a discussion forum) and lose them all. How much depends on your own personal financial situation, but in my opinion it should be at least 0.05 BTC. Since the quantity won't be a significant sum you can play around with some of the lightweight wallets such as MultiBit, Electrum and blockchain.info/wallet and not have to panic about the fact that you are "online".
5. My coins are vulnerable to attack/disappearance anytime I'm using a client/wallet... which is why cold storage/paper wallet is always best - if I have no intent to spend. Am I on track?
Yes, you are vulnerable to attack/theft anytime your private keys are somewhere that someone else might gain access to them. Wallets such as Armory allow you to create transactions without putting your private keys on a computer that's connected to the internet.
1. Clients get robbed/hacked more and more recently, and it seems likely that this will continue being an issue because there can never be 100% security when you're entrusting a client with your wallet...
I really haven't heard much about Armory, Electrum, MultiBit, or Bitcoin-Qt being hacked. Especially if the wallet is encrypted with a password. While it isn't impossible, it is a rather rare occurrence and generally results from individuals installing and running untrustworthy software on the same computer as their wallet.
why would anyone bother using a client, to begin with?
If you want to send a bitcoin transaction, you pretty much have to use some sort of client to connect to the network and broadcast the transaction.
Shouldn't I just stay on the safe side by skipping online storage
Not sure what you mean by "online storage". If you are talking about bitcoin based accounts where you don't have access to the private keys (such as Coinbase, MtGox, BitStamp, etc.) then yes. You should definitely avoid that as much as possible if you want to "stay on the safe side". If you are talking about wallets that connect to peers (such as MultiBit, Electrum, Bitcoin-Qt), then you'll have to make a decision about what you want in the way of convenience and security.
and go directly to paper wallet? (side note - I'm planning to put in very minimal amounts initially, until I get the hang of the whole system.)
If you're just looking for long term storage, then this is a perfectly good option. Just make sure you have multiple copies in multiple locations (wouldn't want to loose your bitcoins to a fire, flood, tornado, etc) and that they aren't accessible by anyone that might want to steal the bitcoins from you.
2. Is there a way to skip having a client and go straight to offline wallet? (sorry if I sound repetitive - I'm just trying to wrap my head around all of this via different wording.)
Yes. Generate the paper wallet offline. When you purchase bitcoins, have the sender send to your paper wallet address.
3. I am soooooo lost re: private keys. All the articles I've read, discussions I've followed and videos I've watched have still rendered me LOST. Say John Doe sends me a tiny fraction of a BTC to help me get started. Now my wallet generates a key for the address John sent funds to.
No. The key is generated first. Then the key is used to generate the address. Then you give the address out to the person that is sending you the bitcoins. A proper paper wallet will have both the private key and the address on it.
I decide to add funds to the wallet by buying BTC from someone on eBay...
Ebay? I'd avoid that, but if you think you can find a good deal from a trustworthy source go ahead. I'd suggest instead that you look at localbitcoins.com
would I have the seller send the funds to the exact same address?
Best practice is to generate a new address for every transaction. You can re-use addresses if you choose to though.
And if so - would I then get another key for that address to replace the first,
If you get a new address for the transaction, it will have it's own new private key. If you re-use an address, then there will not be a new private key.
or would it be two keys for the one address
One address has only one private key. One private key has only one address. They are mathematically linked and you can't change one without changing the other.
or would the key remain the same no matter how many funds add up in that address?
Correct.
And then... why would anyone ever need more than one or two addresses? (I can see having one for saving and one for using/trading/sending/selling, etc... but why do some people have numerous addresses?)
It increases security, privacy, and anonymity. It also helps with accounting. If I give you a different address than I've given anybody else, then any time I receive a payment at that address I know immediately exactly who it came from. If I use a new address for every transaction, then I know immediately not only who it came from, but also exactly what the purpose of the transaction was.
4. If anyone/everyone can see how much BTC each address has, this means that every time you give an address out for people to send funds to, they can go look up how much BTC you already have... right? Isn't that like opening your wallet in front of the cashier and pouring your $ out on the counter for them to see? Or... does that kinda answer the previous question (duh, think I just answered the last question on my own, right? Hence... why people have numerous addresses?!?)
Yes. you figured it out.
5. Please, please... someone just tell me which client/wallet to get started with. The goal is to get it offline, but I really need to get a feel for the system now.
Just to play around with a small amount of bitcoin and get a feel for things, I'd suggest either blockchain.info/wallet (if you want to be able to access the bitcoins from multiple computers/locations), or MultiBit (if you'll only be accessing it from a single computer).
I thought I read that Coinbase is very vulnerable to hacking, other issues and potential future regulation.
Coinbase is an account held by a company (like an uninsuread, unregulated, un-audited bank account). It is not a wallet.
I thought Electrum sounded like a perfect alternative, since it seems easier to go offline with.
For getting started and playing around a bit, Electrum, MultiBit, or blockchain.info/wallet. Look at all three, choose the interface that you like better.
Bitcoin QT sounds good - maybe - but I'm overwhelmed with information at this point.
Bitcoin-Qt is good, but it takes a long time to synchronize and uses up a lot of disk space. You may want to switch to it, but if you're just trying things out it might not be worth the hassle to start with.
