I made the same mistake of buying just the digitizer glass, since I didn't realize how difficult it was going to be. Ended up ruining the LCD on my original equipment. I only spent like 12 dollars, so not a huge loss (missed the return window by about 2 days).
Opted for a new LCD+digitizer from China , waited about 3 weeks, meticulously put it all back together, and when I pressed on the VERY edge of the front screen to adhere the 2mm tape I had laid down (I was at the VERY end) I heard a tiny "pop"....I had cracked the LCD screen. Turning the phone on verified a center line of dead/smeared pixels. Crap. After an almost complete meltdown, I quickly took the phone apart since the tape hadn't fully cured yet, and I had it apart in about 8 minutes flat. I know this phone implicitly at this point.
Ordred from a US supplier on eBay, us-mobilefix or something, for 43 bucks, and they ship SUPER fast out of Kentucky. I got it about 3 days later, I'm in Western NY. Put everything back together in a jiffy, made sure to stay away from pressing anywhere near the LCD area of the screen, and it works perfectly...kind of. No more glitchy issues like I had before, but the quality of the aftermarket LCD is kind of terrible. Even adjusting the color, everything is washed out and seems like it lags/ghosts a little. No longer as bright and crisp. I just accept my fate at this point, as it's now fully functional. Not dumping any more money into this phone.
TL;DR, buy the LCD+digitizer together. Take your time, watch the videos above, BUY THE FINE POINT TWEEZERS AND NYLON SPUDGER, they're invaluable. I just used my industrial heat gun on low, and further away, and it was fine.