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  1. 250k is too small even for a private channel. Why? Because of commit fees (we've talk about that here yesterday). You will be in a position where you could not use your small channel until the mempool fees will not be calm down. You have been warned and you will remember my words.
  2. For a private node (unannounced channels) you should use a good LSP, that have good public routes to multiple destinations.
  3. If you use that node only for SN, then 1 channel with SN node is enough. But what about being able to pay to other destinations or to swap out from that channel? You will depend only on SN node capacity to route your payment to a swap node. Sometimes could fail sometimes not. So in this case you will need other peers with which you can do circular rebalancing from that SN channel. That means you need more liquidity in channels too.
Again, prove what I said: that SN was in a hurry with all this move to p2p wallets is too early because many stackers ARE NOT WELL PREPARED (with funds and also with knowledge). Running a LN node, even a private one, REQUIRE some testing and knowledge.
For your case, using LN only for SN, you are better with a custodial wallet used as bridge between SN and your self-custodial wallets. Read my guides, I've talk about many of them. https://darth-coin.github.io/beginner/getting-started-stack-sats-en.html