Should I replace the front glass and not the whole display?

Front glass only replacement on modern phones generally isn't recommended. To do the job right requires a vacuum table and guides for the wire to remove the old glass, then a vacuum chamber and a UV chamber to replace the glass correctly. I don't know about you, but last I checked none of those things were sitting around my garage. With the OLED screen bonded to the digitizer and front glass, it's a difficult repair even for professionals. To be honest, I wouldn't give you great odds on doing a good job on your first attempt.

That being said, there are kits available that let you give it a shot. I've done it myself when my brother and I tried it out on a couple of older Apple phones; the results were somewhat mixed; one turned out almost okay and the other wasn't so great. They basically looked like badly applied screen protectors with dust bubbles trapped inside.

I get the desire to save that $200, but you can almost certainly do the job yourself for quite a bit less if you use the iFixit guide.

iPhone 12 Pro Max Screen Replacement - iFixit Repair Guide

I realize the screen that iFixit sells costs that same $200, but you can find them substantially cheaper on sites like Amazon, eBay and AliExpress.

So yeah, entirely up to you; I'd suggest you locate a replacement screen in advance before you try your home remedy front glass replacement. Afterward you can judge for yourself if the results are acceptable or not and needs a new screen after all.

@zociax Assuming everything is still working despite the broken glass, then I'd say it is very much worth fixing.

With regard to the back glass, that's always a tough one. If the frame isn't bent or damaged, then yes you can replace just the glass, but it comes with its own set of hazards. The biggest problem is the amount of heat required to soften the extremely tough adhesive that Apple uses on the rear glass. Professional shops use a computer controlled laser to precisely burn off the adhesive but us ordinary joes have to make do with a heat gun. Unfortunately, there are a lot of components just on the other side of that glass and they are prone to damage from the heat. It is not at all unusual for someone to finish up a rear glass replacement only to find that something on the phone no longer works. Plus the wireless charging coil is exposed to the glass so a random slip of the scraping tool can cut that coil and ruin it quite easily.

The absolutely safest way to do a rear glass replacement is to gut the phone; remove everything including all of the flex cables. However, if you're going to that much trouble, why not just buy a new rear housing and transfer everything to it? Based on that logic, I've never done a glass replacement, but instead I replace the entire rear housing.

When looking for parts, you'll usually want to go with one that says it "includes small parts". That means it already has pieces of insulation, bumpers and some flex cables installed when you get it, saving you a lot of time and energy. The only guide I know of for your phone for replacing the housing only goes so far; it assumes, for example, that the wireless charging coil is already installed in the replacement housing. Used housings are sometimes a good choice, but make sure there are pictures showing how much comes with it; if someone goes to the trouble of stripping everything out then they've defeated your whole purpose.

Frame iPhone 12 Pro Max repair - Free guide - SOSav

Something to be aware of if you do decide to do the glass replacement is the rear camera bezel. on iPhones, Apple glues the glass onto the main frame, then welds the camera bezel onto the frame. That means the glass is actually trapped between the lip of the bezel and the frame. It makes it a bit more of a pain to get the glass cleaned out, but the problem comes when you try to replace the glass. If you buy glass that is exactly the same size and shape as the original, you won't be able to install it because it won't fit over the lip of the camera bezel. In order to use that glass you'd have to remove the bezel by chiseling dremel-ing it off or something. Usually the solution to that is to make the glass with a hole for the camera lenses bigger than the original, that way it fits over the bezel. Of course, that leaves you with a much wider gap around the bezel than the original glass had. If it was me, I'd probably try and fill that gap with something like an epoxy that would fill up that space.

Here's an example of a rear housing that would be the easiest to use, but you'll pay quite a bit more for it. Of course, you want to find the right color to match your original.

Replacement for iPhone 12 Pro Max Back Cover Full Assembly - Silver