Man, sorry to hear about your phone!
My daughter-in-law was in a similar situation with her iPhone X; both front and rear glass shattered, but her case was bent as well, so just replacing the rear glass wasn't an option.
I opted to go with a full frame replacement, meaning I had to transfer all the parts over from the old phone to the new one, adding a new battery and a new screen to the mix. The bad news was that there was no guide for me to work from, so I got ambitious and wrote my own.
iPhone X Rear Case Replacement - iFixit Repair Guide
Anyway, it rather sounds to me like you're looking at taking your phone to Best Buy for a screen replacement. That's a perfectly viable solution, and if your rear cameras haven't been affected by the damage and you're happy with living with a case as the solution to the cracked rear glass, then hey, it's all good!
I wasn't clear on exactly what you meant by the front camera being cracked though. I'm taking it to mean that the display glass over the peephole for the camera is cracked and you're seeing that on the camera's view, but correct me if I'm wrong. If the lens on the camera itself is cracked, that's a whole different story and may or may not be repairable. On older phones like the X through 11 at least, you can replace the front camera and still keep Face ID working, but Apple is locking things down more and more, so I don't know if that's going to hold true on the 13.
On to your main issue, that of replacing the screen. You've got a lot of options open to you, and I'll try to cover them all. Here are the issues people have encountered when replacing the display on an iPhone 13.
- Unless you are an Authorized Apple service provider, changing the screen will result in getting a pop-up message on the screen for about a week warning you that your screen may not be genuine - even if it is a genuine Apple screen.
- True Tone function will be disabled. On previous iPhone versions you could reenable True Tone by copying a bit of data from the old screen to the replacement using a device programmer such as Qian Li's iCopy. I do not know for sure if that is still possible with the iPhone 13.
- If you are running an early version of the iOS 15.x system, Face ID will also be disabled. However, updating to iOS 15.2 or newer will restore Face ID.
As you've already hinted at, you can certainly take it to Best Buy and have them replace the screen. Ask them up front if they're going to be able to restore True Tone and get rid of the genuine part warning. I'd also ask what kind of screen they'll be replacing it with; the ones on the market consist of soft OLED, hard OLED and LCD screens. Soft OLED is what originally came on the phone. Hard OLED is a little cheaper but the picture doesn't extend to the curved edges of the screen, so it will be marginally smaller than the original picture. LCD is the cheapest, but will be thicker than the original, will take more power and the display quality probably won't be as good.
Those questions should be asked of any repair shop you decide to use. The only way to be 100% sure that everything will work like the original is to either take it do an authorized Apple repair facility, or utilize the Apple Self-Repair program. Expect to pay quite a bit even for the self-repair option, as you have to buy the screen from Apple and rent their equipment to do the repair. But if you go that route, you won't have any messages and everything should work just like new.
Of course, this site is all about fixing your stuff yourself, and @jmehnert has already pointed out the guides you would need to do your own repair. Again, the downside is you'll get the genuine message and unless you buy a device programmer, you'll also lose True Tone function, but overall that will be the cheapest option available to you, plus you'll be able to compromise on what kind of display is good enough for you versus the cost of the various kinds you can get.
Finally, with respect to the broken rear glass, there you have two options; you can either replace the glass or you can replace the entire housing. Each one has it's advantages and disadvantages.
With replacing the glass alone, you've got your work cut out for you. You'll need a heat gun to soften the extremely strong adhesives Apple uses for the rear glass, and you'll have to painstakingly chip out all of the glass from the rear of the case, taking car not to damage the wireless charging coil and the cameras. The camera peepholes are a pain to deal with as well, since they actually overlap the glass. There are two ways of dealing with them; the first is to break them off the rear case (they're spot welded on) in order to be able to place the glass, then figure out how to resecure them once the glass has been replaced. The other way is to buy a rear glass where the hole for the rear cameras is bigger than the original in order for the glass to fit over the camera housing without having to remove it. That has the downside of leaving a gap where liquid and dust could enter the camera. You can probably mitigate that somewhat by using some sort of sealant around the camera bezel before setting the glass down; that should help seal it up.
A professional shop will actually use a laser that's programmed for the exact model of phone to burn away the adhesive so as to minimize the amount of heat the interior components are exposed to. There are several places that offer rear glass replacement services, so that's always something you could pursue at some point in the future when you've recovered financially from the screen replacement, lol.
A downside to using a heat gun is that it's not uncommon for the amount of heat needed to replace the glass to damage internal components in the process. Although most of the time there aren't issues, we have seen examples of flex cables and other parts that no longer work after a rear glass replacement. The only way to absolutely ensure no damage is done to the parts would be to remove them before starting the glass replacement. That means gutting the phone; removing everything inside for safety's sake. However, if you do that, you might as well just replace the entire housing since you'll have everything out anyway!
Okay, I've rambled on long enough; hopefully that'll give you some food for thought and let you figure out your options. Good luck with it, and let us know what you decide and how it goes!