I already hold one current account with Halifax, would Lloyd's be a good 2nd?

The recommendation on here is typically to have current accounts with more than one banking group in order to offer protection against your money being unavailable either accidentally (e.g. system issues, etc) or deliberately (e.g. accounts being suspended, etc), but, as Lloyds and Halifax are both part of Lloyds Banking Group then the value of having accounts with both of them would be limited, so you'd be better going elsewhere for your second.

Basic bank accounts are intended for those who can't get a full current account, so if you already have a current account then it's very unlikely that any bank you apply to would offer you a basic account, i.e. if they decline your application you won't be offered a basic account in lieu of the better one as you'll have to declare your first account during the application process.