So, I've been busy over the last week but I meant to return and talk a little bit about what I recommend on the subject and how I go about it.
Also, please remember, I say this as a kid who read Herodotus' Histories and Gibbon's Decline and Fall of the Roman Empire, etc., so I don't say this as an outsider looking in but rather as someone who has made some mistakes and wants to share the experience. In short, I think reading the "classics" on history is a pretentious waste of time. It's meant to sound impressive, to make the reader sound like he has read The Great Books of All Time and is an Incredibly Knowledgeable Person, but it doesn't really leave you with a good idea of the events and how the modern world developed.
It's one thing if you want to watch how the study of history has changed over the centuries (or even decades, recently). In that case, seeing the very different approach taken by ancient authors to more modern voices is instructive. Leaving aside the stylistic and language barriers (and even for works in English, there are still some) for a moment, classic works aren't going to give you a better insight into the facts than a modern work. Some of these books were pushing a particular narrative of the time that colors the work (i.e. Gibbon and his whole deal with Christianity). Some do not have access to all the facts (picking on Gibbon again here, his understanding of the "barbarians" is terribly wrong, modern scholars like Chris Wickham and Guy Halsall are far better to consult on the subject; same analogy can be drawn for Tuchman and Strachan). Some works are simply not as rigorous as a good modern work or make assumptions that have turned out to be false (here's where I want to compare Tuchman on the opening German war plans of WW1 and Strachan). I can ramble on, but I think you guys get the picture.
The problem for a new reader of history taking the first plunge into history is that he is not fully aware of the overall historiography (how we think about history). He's not aware of how the scholarship has changed over the last few decades. So the new reader picks up a "classic" and may have a pleasurable time reading the work, but ends up with a bunch of obsolete and false assumptions, incomplete facts, and with an unconscious bias towards the subject matter.
By contrast, solid modern works include sections on comparing theories and comments on the historiography, so at least the reader is aware of its existence. Good modern scholarship will be up-to-date on factual evidence and at least not contain flagrantly incorrect assumptions made decades ago. That's not to say it's perfect--it isn't, there will still be things that are fixed in future research, but at least you aren't starting from a place that is known to be wrong.