FWIW, comprehensive claims do not have direct effects on your insurance rates (as opposed to collision claims). They might affect your underwriting, so if you are generally not a good driver, it's still likely better to not make a claim. But, if you have a clean record with no other claims, go ahead and make the claim. Typically you can ask for a check for the net payout amount. If it's a 2k repair and a 500 deductible, you'd get a check for 1500. It's your choice on whether to repair the car or not, but if you don't, then your insurance company will reduce the value of your car to them by 2k. (So even though you peg it at 8k, if you were to pocket the money and then total it in a month, they'd only pay you 6k.) You typically have to prove that the repairs were made if you want to claim damage to the same area either with a repair shop bill or allowing an adjuster to verify your DIY repairs.
So, when a deer ran into my wife's car, it only cracked the fender, which after replacement and painting would have net about $850. We happily took the check and invested it.