Yay, a home bar post! I've just recently been stocked my own home bar (with Sage's help of course) and would be happy to lend my own personal experience to help out the cause.
First of all if you're going for completeness I would try to have represented each of the six major categories of base spirits: Vodka, Gin, Tequila, Brandy, Rum, and Whiskey (which can be further subdivided into Irish, Scotch, Bourbon, Tennessee, and Rye). Having a good bottle of each of these (not as essential on the different sorts of whiskeys, as they are less frequently used in cocktails) will pretty much ensure that you can make whatever your guests want.
In addition to the base spirits, then, you obviously want to cover your bases as far as mixers/cordials/liqueurs go as well. There are tons and tons and tons of these, many of which are only used in a couple of things, if ever, and there's no way you'll ever be able to have all of them (unless your bar is freakin huge and your wallet is too) but there are several more common ones that do get used pretty regularly. You've mentioned triple sec already, this one is definitely important. I'll get to brands later on. Also in my home stock are curacao (orange and also blue for the occasional crazy blue drink, they taste the same but some drinks call specifically for the different colors), creme de cacao, and creme de menthe. I also have irish cream and creme de cassis, but unless you have a friend who specifically likes something involving those you probably wouldn't use them much.
Then after you've got standard spirits and mixers covered you might want to branch out a bit into the liqueur area with things like Grand Marnier, Benedictine, Campari, things of that nature... but this is really just going to be a personal preference sort of thing and completely unnecessary. Cointreau is a very nice quality triple sec and some drinks just wouldn't be the same without it, but it is again not necessary.
As far as brand recommendations go, here's my personal list, but these are definitely personal preferences and your own are probably different from mine.
Vodka
Recommended: Finlandia, Pearl, Absolut, Skyy
Not Recommended: Luksusowa, Stolichnaya, Grey Goose, VOX
I find the Finlandia to be consistently the best, tasting like... well, water, which is what vodka should taste like, as it is simply straight alcohol diluted with water. Surprisingly I found GG, Stoli, and Luksu to be quite distasteful, especially the Luksu which to me tasted like water that someone squeezed a potato over.
If you want a completely decent cheap vodka, Gordon's is both of those. Finlandia, my favorite, is not terribly expensive, and certainly beats stuff like GG pricewise.
Gin
Recommended: Bombay Sapphire (for martinis or drinks that feature the gin), Tanqueray (for cocktails and drinks that you want to make sure that the gin is not overpowered by the other ingredients)
Not Recommended: Seagram's
Gordon's also makes a completely decent cheap gin.
Tequila
Recommended: Sauza Hornitos
Not recommended: Sauza Silver, Jose Cuervo gold
I'm not especially experienced with tequila. Generally for mixing you want a lighter tequila (though the Hornitos is nice and light while still mellow from a bit of aging) and the darker anejos should be saved for sipping.
Brandy
Recommended: Raynal VSOP
Not Recommended: Martell VS
The Raynal is quite tasty and also quite cheap. E&J VSOP is also totally decent. For a good mixing Cognac I'd recommend Salignac, which is also nicely inexpensive.
Rum
Recommended: Gosling's Black Seal, Appleton Estate V/X, Myer's Dark
Not Recommended: Anything in Bacardi's entry-level, though the darker Select is a LOT better than the clear Superior which IMO you should AVOID at ALL POSSIBLE COST
. Also I find the Malibu coconut rum to be way too industrial tasting, but some people apparently dig it a lot.
With rum you generally want to have a good light/gold rum (Appleton Estate V/X is in this category) in addition to a darker rum (Gosling's or Myers). Some people like Captain Morgan's, some people like a good mellow sipping rum. For this I would recommend Cruzan Single Barrel Estate. My personal own best rum experience ever is with Pyrat XO Reserve, though this rum is rather pricey (but completely worth every cent!)
Whiskey
Recommended: Maker's Mark Bourbon, Wild Turkey Rye
Not recommended: Canadian Club blended, Jim Beam Rye
I'm not so much of a whisk(e)y fiend, and I probably wouldn't know a good scotch or irish whiskey if it bit me on the butt, but I have had experience with Ryes and Bourbon to a degree, which is really all you're going to need if your focus is cocktails anyway.
That's pretty much it, I hope this can help you out with your new home bar and that you have as much fun with it as I have with mine!