OP, it's your choice whether to accept both the check, and the risk of it not being good. You could insist on a money order from USPS.
Since I fired my ISP, I'm using a browser access from my phone. It's not a smart phone. In fact, this phone compared to Jethro Bodine, would to make the latter look like a Rhodes Scholar.
ebay mobile is no longer supported on this browser, along with some other websites. PITA, but I deal with it.
I have had dealings with AK'ers through Barter town, and give them the option of personal check, or USPS money order. Paypal isn't an option for me. For some that may not be ok for them, and that's ok by me. Others are fine with either PC or MO. Personally, I don't mind if they want to delay shipping until either the MO gets cashed, or my PC clears the bank. I know the check's good, and they will also find that true.
You may be dealing with an upstanding, honorable citizen, or you may be dealing with utter bottom dwelling gutter garbage.
I'm not suggesting you should accept a personal check from someone whom you've no previous dealings. If you suggest them sending a USPS money order, along with delaying shipping UNTIL it is verified and cashed, and meet with no teeth-gnashing, woe-is-me...you-don't-trust-me B.S. sob story....it just might be a true-blue John Q. Public.
Ultimately, it's up to you, and do what's in your best interest. If you're not comfortable accepting personal checks, or money orders, then let them know and don't lose any sleep over your decision.
For transparency's sake: I have no affiliation with this sale. Just offering a different perspective.