?Monthly Tickets for London Public Transportation?

Wait till you get to London then purchase an Oyster Card. It has a refundable deposit.

"Recall hearing about one that had to be purchased before arriving."

Don't buy anything for transport around London until you get here.

There are monthly passes that you can load onto your Oystercard, but what pass you need (ie: what zones), and whether it is cheaper than individual tickets or day passes depends entirely on your plans. https://tfl.gov.uk/fares/find-fares (there is no tfl.gov as posted earlier)

To clarify, the Oyster is an electronic wallet rather than a pass, although some passes can be loaded onto (into?) it. The one financial advantage is a limit on the cost of travelling in the central area per day. Pass the limit and you ride free for the rest of the day. It certainly makes entering and exiting the trains simpler while deducting the correct fare in this zoned system. Yes, consult Transport for London (tfl) as suggested above. That site is good for determining routes, too.

There is relatively little extra saving for monthly travelcards over weekly, and with weekly capping on a contactless debit/credit card you get the same anyway.

Are you alone or part of a group - and what kind of travel pattern do you expect?