For example, I have read about instances in which an LN node failed, the user restored from a backup that did not have the correct channel state, which resulted in the backup-restored node trying to close the channel via an old channel state.
You're right. Although, it's fairly uncommon to run an old backup unintentionally. LND by default generates only static backups, which can be only used to request the other party to close a channel. C-lightning's backup plugin backups the whole channel database to a remote directory/drive and it constantly overwrites old backups.
What's the best channel_capacity/network_contribution ratio? For instance, would it be more contributive to open 100 of 0.01 BTC rather than 2 of 0.50 BTC?
100 channels sound better. If someone undercut (in terms of fees) either of your channels, it would greatly impact your routing effectiveness. Also, you are more likely to get more routing attempts through you as long as you choose channels and set your fees reasonably
Also, how do I choose the proper nodes to do this?
That's one of the trickiest parts of running a Lightning node. I usually select some random medium-sized nodes from either
amboss.space or
1ml.com and then check the shortest path from my node to theirs using
lnrouter.app. Remember that path finding algorithms also take the route length into consideration.
Also, how do I choose the proper nodes to do this? I had read about triangles, but I'm not sure if that's what I'm talking about.
You can learn about liquidity triangle/square/pentagon swaps
here. Once you set up a mainnet node, you can use that website to find partners for the swap. Liquidity swaps might actually improve your routing performance.
Yesterday, I performed a triangle swap with two other bitcointalk members. Each of us opened a 0.05 BTC channel to the other person. This way, we gained additional 0.10 BTC capacity, which means that this swap has doubled my node's capacity. I paid 222 sat for the opening transaction. We dropped the fees to 0 and TheJuice's script took care of the rebalancing. On the same day, I routed 6 transactions from the channel I opened and I got paid 222.76 satoshi. The channel paid itself off in just a few hours.