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Is it better to open a channel the first time by swapping from on-chain BTC to my new Zeus LN wallet
You can open your own channel (and emptying it to receive more in the future) or just order an Olympus channel from within the app beforehand.
by sending a Lightning transfer from the exchange directly?
Maybe it's just my preference but, one bigger channel is better than having multiple smaller channels.
When opening a channel I think it will need to be large enough to accommodate the maximum balance I plan to hold on Zeus LN wallet at any given time, not just the size of the periodic transfers from the exchange (= rather than a 250,000 sat size channel I should do 1,500,000 size?)
Yeah, when you already filled up your channel you can just do one swap out to onchain thus bigger payment size would be better
But once I transfer out my larger UTXO (maybe 1,250,000 sats) and my LN wallet is now only holding 250,000 sats, what happens in the coming weeks when I build up again to 1,500,000 via new LN transfer to Zeus?
You would have a lot more receiving capacity
I read somewhere that it would not matter that I initially opened a large 1,500,000 channel, by sending on-chain I would have my channel reduced and basically have to open a new channel again every month or so to accommodate the new balances.
Zeus (LND) didnt support splicing yet dont worry about it