Hi Rita,
I think you have a overly simplistic understanding of digitizer repair. The digitizer is bonded to the LED and requires rather specialized skills and equipment to successfully replace. At a minimum you'll need a vacuum chamber, a vacuum machine for holding the screen and possibly UV equipment to cure the OCA. I'm very experienced at phone repairs and it's something I wouldn't tackle without a really good reason, and the price difference between a screen assembly and a front digitizer glass isn't nearly enough for me to attempt that repair.
Really, as far as practical repairs us DIY-ers can do, the choices you have are to replace just the LCD/digitizer/backlight assembly, OR replace the screen + frame assembly. There are advantages and disadvantages to either.
With respect to just replacing the display without the frame, it's going to be a little bit cheaper, but not all that much. It's somewhat difficult to separate the LCD from the frame, but since you're only talking about the old display, being careful with it isn't a high priority since you'll be throwing it away anyway. You need to do a good job cleaning and replacing the precut adhesive to ensure the screen sticks to the frame and won't fall off.
Samsung Galaxy Note 8 Display Replacement - iFixit Repair Guide
On the other hand, you can replace the complete display + frame assembly. It will cost slightly more and it is more work as you have to transfer everything from the old frame to the new one. However, you are assured that the screen will stay securely on the frame and not worry about it falling off, plus you don't have any worries about damaging the screen when mounting it on the frame.
Samsung Galaxy Note8 Display Assembly with Frame Replacement - iFixit Repair Guide
It's up to you which way you want to go with it; take a look through the guides and decide which one you want to use.
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