According to https://en.bitcoin.it/wiki/Scalability "VISA handles on average around 2,000 transactions per second (tps), so call it a daily peak rate of 4,000 tps. It has a peak capacity of around 56,000 transactions per second".

Supposing SegWit is operational, and all the OP_CODES needed for a full implementation of Lightning Network are also operational, what would be a good estimate for how large a block has to be in order to support as many transactions as Visa?

More specifically: What kind of transactions would have to happen obligatorily in the blockchain? Monthly salary payments to fund the channel, for instance? What else?

What about VISA + all other major credit cards combined + 90% of cash payments world wide?

Bonus question: If the block size required for all of these becomes too large to become desirable, what is the next trick we can use in addition of LN? Sidechains?