As a renter, I expect fresh paint when I move. I lived in crappy places and frontdesk/elevator condos...all had fresh paint. Sometimes it was crappy white paint, but it was new. If you decide to rent I would repaint. Re the sink...are the racks built in or is just one you get at Target and place in the sink? If the later, just buy a new one. They’re like $15. Otherwise make sure all your sinks are clean and rust free during showings; they don’t have to be brand new. For blinds...just don’t get those ugly roll down ones.
We viewed a large, “updated” (granite counters, stainless steal appliances, dishwasher) condo for rent that was below market and had a rusty sink, soap scummed bathtub, and general wear & tear on paint. It was a good deal but we passed because of the concern that those fixes are pretty minimal, and if the landlord doesn’t do the most basic of things between tenants then how awful will they be when a more serious repair comes up? (For reference the place we picked has outdated appliances, laminate counters, no dishwasher, and a small, ugly, yellow 80s bathroom sink. But it was all clean, in good order, and had new paint & blinds that showed some care.)
That said...you started this talking about the fridge. When you say it’s dying, how long do you think it can eek out? Like it’s not as efficient anymore, but will keep food cold for years to come? Or it could die at anytime? Because if fridges are standard in your market (as here), it’s standard in the lease that you’re responsible for maintaining and replacing it. So it’s not necessary to have a new one, but you better be prepared to drop everything and get in a new one ASAP if it dies during the lease. It’s up there with heat, hot water etc in terms of things your tenant will legitimately demand you get on top of immediately. You won’t have time to watch out for a good deal. You’re stuck with what’s available at the time.