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you can run a node without any bitcoin at all.
a node is just a program you run on a computer that tries to download and verify all the blocks in the chain with the most proof of work. once the program has verified all the past blocks, it listens for new blocks with valid proof of work that add to that chain.
While it's waiting for a new block, the program also listens for (and can relay to other nodes) unconfirmed transactions. The place it saves these on your computer is called your "mempool."
That's pretty much all a node does, be it Core, Knots, or libbitcoin.
A wallet keeps track of the coins that are controlled by your keys. Wallets need to talk to a node to know which blocks have transactions that are relevant to your keys. If you aren't running a node, your wallet software has to ask someone else's node -- and this means it tells them which coins you are interested in (by which they can infer that they are your coins).
you can run a node without any bitcoin at all
I'd go further: anyone who wishes to dabble, and doesn't plan to accumulate any significant amount of coinage[1] should possibly spend their time more wisely[2]; whereas anyone who plans to pay for their first major chunk of Bitcoin should already be running a node, so that they don't e.g. buy testnet, or one of the altcoins whose wallets can trivially be reskinned to fool a newcomer.
I think I see where my confusion is. A lightning node requires staking for liquidity. Ergo, that's where I got the idea of a bitcoin node requiring a cost.
"Staking" sounds like a carryover from shitcoinery. You can run a lightning node all you like regardless of funds. It would be pointless, but it is a fact. This is where you should probably read @DarthCoin primers on private vs public lightning nodes and understand the purpose of channel openings, inbound/outbound liquidity and routing (if public).
I sympathise with your hostility for "nothing at stake" shenanigans, although from the perspective of someone figuring things out for the first time, who might have first heard about trust-minimized finance from proponents of e.g. ethereum, there is not an obvious difference between staking ethereum and improving the lightning network by adding liquidity and running some LSPs.
This hostility is a protection against stupidity.
Correct me if I'm wrong (probably), but don't you need a certain amount of Bitcoin to run a full node versus just be a core wallet?