The fairest way to do I think would be to have a lottery system. Where you would be able to apply for tickets over a week period and then they are randomly assigned to groups. If people then don't pay the deposit within a week or two some other group would get the tickets.
The thing I don't like about the first come first served is that if one thing goes wrong then you could fail to get tickets eg, power cut, internet cuts out or computer crashes.
Also many users may not be confident using online services. Especially in the resales when you have to pay all up front there's a lot of money changing hands, there has to be a few cases where people have been caught by scams thinking they are buying a ticket. I haven't seen any accessibility options on the site either.
The lottery system won't get them as great headlines as, "sold out in 27 minutes". But I think it would be a less stressful environment, that doesn't rely on everything working for an hour on a Sunday morning