City travel passes

In Paris you can get a carnet, which is a 10-pack of subway/bus tickets for 14.10 euro, that may cover the both of you for 4 days. If not you pick up some extras at 1.80 euro each.

"I am planning on purchasing the tickets from the country's train website. Is that the best?"

Usually, yes. Some exceptions are Spain and France, where the country's websites can be hard to use with foreign credit cards. For France, if you can't get SNCF to work, use https://www.capitainetrain.com/. For Spain, if you can't get RENFE to work, start with the tutorial on TripAdvisor; in there are links to other sites that you can try instead: http://tinyurl.com/cu48wk5

"I was wondering if city travel passes are worth purchasing"

For London, most feel the London Pass is a bad deal. And you aren't in London long enough to get value out of a 7 day Travelcard, so just use an Oyster with Pay As You Go (it will "cap" each day at the one day Travelcard price), unless you want to use the two for one offers from Days Out (ask if you need more info about these).

For Paris, there are three products: the Paris Pass, the Paris Visite Pass, and the Paris Museum Pass (yes, it is confusing). A Museum pass can be a good deal if you're seeing a lot of museums, or want to visit a large one (like the Louvre) in sections over different days. The other two are poor value for most people.