If you live in an area like you do with trashy streets just shredding tires and or getting numerous flats I would be less concerned about speed and more concerned about durability, save the fast tires for racing or fast group training rides if you're involved in that sort of thing, and get the tough tires for everyday riding and or commuting.
So what's a tough tire you scream, there are several, probably the best one for warding off flats and tire damage is the Schwalbe Marathon Plus however it is the most heaviest of the tires, next one would be the Schwalbe Durano Plus, followed by Bontrager Hard Case which is on par with Specialized Armadillo All Condition and Continental Gatorskin Hardshell, all three of those last ones are lighter in weight then the first 2 though the second one is darn close, and those last 3 offer the best flat protection you can get from any other tire OTHER THAN the first two I mentioned.
You could use a liner but I've found that all plastic liners like the Mr Tuffy not to be as great as people think, I've had goatheads (which is a desert found plant in the Southwestern US) to penetrate a Continental Gatorskin WITH a Mr Tuffy. The only liner I've found that I liked and I can prove it's tough is the Panaracer Flat Away, problem with that liner is that it's expensive at $15 to $18 each and it can only be used one time, when the tire is worn out you throw out the tire with the liner; but it does stick to the inside of the tire so there is no liner flopping going on inside the tire which raises doubt if the liner stayed in exactly the right position every time you have to take the tire off or installed the liner for the first time like the Mr Tuffy. Also if you're using high pressure road tires Slime sealant does not work once you get past 70 psi, however there is a new trick you can do as a flat slime type of thing, you can use Stans sealant in a non tubeless tire, meaning in a tube, and supposedly this stuff works really good against flats as long as the tire keeps rotating after initially being punctured, but I haven't tried it not do I think I will.
Thicker thorn resistant tubes can help to the smallest degree of what other forms of protection can help.
Personally if you get a really good flat resistant tire like I mentioned above you won't need goo or a heavy tube. Once I switched to Specialized Armadillo All Condition tires when I use to live in the Mojave Desert of Southern California where the goatheads were flatting me 1 to 3 times a ride all flats stopped and all I had inside the tire was a Specialized Turbo tube and no liner or goo. Since I moved from that region I no longer ride on trashy streets so I no longer use the Armadillos, instead I use pretty much standard road tires that I find on sale, though my touring and commuter bike I do use the Panaracer Flat Away liner but I only use it on the rear since the rear gets most of the flats and it's a pain to fix a flat on a touring bike with fenders and panniers on the tourer and I use it on the rear of my commuter so as not to be late to work due to a flat. However if I were to do a tour across the US I would get a pair of Schwalbe Marathon Plus.
