Well, for starters, let's clear up some terminology here.
GLASS - the uppermost layer, what your fingers touch. This is the glass. Just glass. Usually color bonded bezel, with or without markings for capacitive buttons, cutout for home button etc.
DIGITIZER- Just bellow the glass, this is a thin, transparent layer, typically also made of extremely thin glass. This is what senses touch input, and translates it into readable data for the phone. Often times, the glass and the digitizer will come bundled together, pre-adhered to one another. If there's any chance that the digi must be replaced, its always best to go with a glass+digi combo, as adhering the two together is near impossible without special equipment. Plus, the glass+digitizer combo is general not much more expensive than just the glass itself. Other phones, such as Samsung Galaxy phones, have the digitizer built into the LCD/screen, instead. Determining how a specific phone is built before planing a repair and purchasing parts is always a good idea.
LCD/AMOLED/SCREEN - This is the part that actually displays the image. It, too, is mostly glass, and still extremely thing (paper thin, even, on some phones).
Finally, Some screens have the BACKLIGHT built in, such as on Samsung Galaxy phones. Other phones, such as (mainly) iPhones, have a separate backlight that goes on the very back once the glass+digitizer+screen have been bonded together.
So we have the GLASS then the DIGITIZER then the LCD/SCREEN and finally the BACKLIGHT. All of these elements combined, form a DISPLAY.
Finding and ordering parts can be a huge pain in the ass, with all the misused terminology, so it pays to be extra sure.
Now, how hard is it to replace a DISPLAY varies by phone, I would say a 5-7/10 difficulty, generally. It can be quick and easy, such as with iPhones, BUT something as small as switching a 1.3mm screw for a 1.1mm screw will render the phone permanently dead.
Glass only repairs are one of the most difficult, and labor intensive repairs there are. It's a 10. Unless you have a good deal of mobile device repair experience and a serious interest in a career in mobile device repair, I would not recommend attempting it. Especially not to save a mere 60 dollars - you will need at least that much worth of tools, glue, and supplies anyway. Do yourself a favor, and purchase the FULL DISPLAY. While not the easiest, it is still a manageable repair job for a novice. Better to spend a bit than almost certainly end up with a sticky pile of glass shards and junk.
I have been doing mobile phone repair for over 5 years, and I can assure you that glass only repairs are best left to professionals.
Just by purchasing the full display, and replacing it yourself, you are still saving quite a bit of money vs paying a repair shop to do it, so don't feel like you're missing out :)