i recently read Thomas Pakenham's The Scramble for Africa: White Man's Conquest of the Dark Continent from 1876 to 1912 and i was completely fascinated. for 700+ pages i was enthralled by the tales of European explorers and military expeditions sent to map out and carve up vast swathes of Africa in the name of imperialism.
shortly afterwards i also read David Grann's The Lost City of Z: A Tale of Deadly Obsession in the Amazon (now a major motion picture!), which furthered my newfound interest and obsession with Victorian (or Edwardian) explorers.
i found the frequently starring role of the Royal Geographic Society in both of these books to be one of the most interesting parts, and my imagination ran away with itself thinking of meetings of now-famous explorers and naturalists meeting at 1 Savile Row, smoking cigars and drinking brandy over hand-drawn maps of foreign lands with ever-shrinking blank spaces. i am extremely interested in learning more about the RGS and its history, and particularly their contributions to science as well as their efforts to help expand the borders of the Empire.
part of my interest is admittedly less academic than it is romantic. from this subject i get the same feeling as i did as a child reading fiction like Rudyard Kipling's stories of colonial soldiers and big game hunters in the British Raj or even James Gurney's fantasy series Dinotopia. i want to feel the wonder and excitement of a 19th-century European 'discovering' the wonders of Africa, South America, and Asia for the 'first' time.
a few searches on Google and Amazon produces disappointingly few results, so i thought i'd turn to this lovely forum for further recommendations. i no longer have access to a university library, but i have had pretty good luck with my local municipal library's inter-library loan system, so hopefully i'll be able to find a copy of anything that is suggested.
I wish I had more time, or I could dig into this--I have worked on the Society; I have worked at the Society (in the Archives); and I'm an FRGS myself, as an academic who works in the field. The Society did a lot of remarkable work in popularizing exploration and travelogues, as well as accessing the world for Victorian popular and learned opinion in ways that would strongly tint imperial expansion. The various Fellows and officers of the RGS also occupied key positions in government and arguably drove the development of a science of geography for colonial aims.
One book you absolutely must read is Felix Driver's Geography Militant: Cultures of Exploration and Empire (Oxford: Blackwell, 2001). Graham Burnett's Masters of All They Surveyed (Chicago: U Chicago Press, 2000) is another that touches on the whole. Historians of geography and cartography also hit Godlewska and Smith, eds., Geography and Empire (1993?) for various chapters and Bell, Butlin, & Heffernan, eds., Imperialism and Geography 1820-1940 (Manchester: MUP, 1995) as our old touchstones. I suppose more recently, Robin Butlin's Geographies of Empire (2009) should include some of this material, along with many issues about geography and empire that are not in your field of vision. Dane Kennedy's The Last Blank Spaces: Exploring Africa and Australia (Cambridge: Harvard UP, 2013) also hits the RGS, including slightly wider periods, and is the freshest; I'm a fan of his critical work. There are many other studies of travel writing that tend to include the RGS in some form, because it was the vehicle for gaining legitimacy as a geographical and scientific traveler at the time, perhaps too many to list here. Driver and Kennedy are absolute musts, I would say--they tell interesting stories to make useful points, even though they can never be exhaustive.
I always found it humorous that the Institute of British Geographers, which now is attached to the RGS, published an essay in its 1998 Transactions (Barnett's "Impure and Worldly Geography") on the development of discourses around Africa up to 1873 through the RGS as inheritor of the African Association. It's worth reading, despite its age.
[edit: fixed the Barnett link.]
I'd recommend using one of your slots on JSTOR's shelf for this essay. It's a look at the RGS through a military lens during WWI, which I think is a nice tie in to Percy Fawcett's adventures. Lost City of Z grabbed my interest pretty quickly as well when I found it in a Christmas stocking this past year.
Also available on JSTOR is The Journal of the Royal Geographical Society of London which is cool is you're looking for something from the horse's mouth in the era you're interested in.
As far as being interested in the romance more than the academics, I'd recommend giving Paths of Glory a shot. No, not that one. This. It's a novelization so take note of that obviously and Archer has his own take on whether or not George Mallory summited Everest.
You might be interested in Sir Samuel Baker, some of whose books are over on Project Gutenberg. He was a civil engineer from a wealthy family, did a good bit of exploration of the Nile and inner Africa, sometimes for the RGS. And ( if he was to be believed) rescued a Romanian slave girl from a market in Ottoman-occupied Bulgaria and made her his second wife. But he also spent time wandering around with a gun , hunting. At the time big game hunters would be using guns firing low-velocity but massive round balls, and the recoil from these things (not far from cannon) was incredibly punishing, so it's hard to think anyone would enjoy it but he did. His Wild Beasts and their Ways is filled with black powder smoke and the demise of large mammals.