I would lube it first with ATF (automatic transmission fluid, which I use all the time on my bikes) and follow that with gear oil, to see if you can't use the existing chain and sprockets.
Your wife will not want you to use either of these once you have determined if you can use the bike as is; shift to a lube that isn't messy at least for her bike.
I like ATF because it does not hold grit like most oils, and, it has additives that should help the o-rings. But it is messy! Equivalent to 7.5 wt oil in its viscosity. I still use it for fork oil (this dates me, pretty much).
I would use kerosine (not gasoline!!!!!) and a nylon brush (not wire brush!!!!!) to attempt to remove the rust. Likely, with such low miles, it is just surface rust and hasn't penetrated the rollers. Look it over after cleaning it and make sure there are no binding or sticking links, and it should be ok. I also assume that with only 1000 miles on it the sprockets are perfectly fine, unless during that period for some reason the chain was waaaaay overtightened (many new riders will do this thinking any chain slack and it might fly off), and the teeth are hooked because of it.
After cleaning the chain, while oils will lubricate the chain very well, they also attract grit and dirt and fling off more than drying lubricants. I personally like the Original Bike Spirits chain lube, because it has tons of moly and dries to a waxy coat, which repels water and doesn't get sticky. Any lube that doesn't get sticky should be fine. Gear oil/tranny oil can be used in a pinch if needed, but will require a good cleaning with kerosine before reapplication later, particularly if you're in a dusty environment.
Welcome to the site!
If it were me, I would probably replace that drive chain. While it's hard to see the rollers in your pic, I'm guessing they are just as rusty as the side plates. And so running a chain with rust pitted rollers would more than likely accelerate wear on the sprocket teeth.
Here's a good quality RK 520 O-ring drive chain on Amazon (I've been running the same RK chain on my Honda XR400R with no issues) and is the correct length for the CBR250R: https://www.amazon.com/RK-Racing-Cha...20+drive+chain
all good advice..
you could also use new parts
while cleaning and soaking etc
the original, if otherwise ok,
for an emergency/spare..
[if you/she think that way]
you just dont know what its had
or not had done to it.. best bet
ditch/replace oil as recommended,
or any fluids etc, you may suspect..
clean sheet, as they say..
First off, thanks for all the replies. I do appreciate it. I took a couple better pictures of the chain in better lighting.
Since my wife is going to be on the bike, I think i'll just outright replace the chain. I mean, it's $40 lol. Thanks for the link! I'll leave the sprocket alone. I'm sure it's fine.
As Schroeder mentioned the possibility of the engine oil being original, or even if it was changed at the 600 mile service it's likely the oil is at least couple years old now (which wouldn't surprise me on a 5 year old bike with 1000 miles), I'd also recommend doing an oil & filter change right away.
Make also sure that the bike has had it's 600 miles service done. With two previous riders and just 1.000 miles it's possible that both thought it unnecessary and you still have the original oil in there.
Besides I think some of the bikes had valve clearance problems that had to be remedied at that service.
The fluids were changed a couple times at least. Regardless, I'm going to change the coolant and oil both and make sure they're new. Standard stuff.