How much are are renting the property for would influence my design decisions. For frugal/quick decorating:
1. Clean cabinets with something like Krud Kutter. Try Restore A Finish in the best matching tone - it may be enough to do the trick. You can also buy a very similar shade, but something that would tone down the orangey tones in wood and try a small test spot on one of the insides of the cabinets to see how it looks. The Restore A Finish has a small amount of stain and works well for covering small scratches/wear and tear. I have no idea what kind of wood it is.
https://www.homedepot.com/p/Howard-Restor-A-Finish-16-oz-Walnut-RF4016/100199071
2. It's hard to tell from the photos if the original pulls are copper colored, but a straight pull might look better. Be sure to check out Ebay, Habitat ReStores, and the multipacks sold at Lowes/Home Depot. You might try one in an oil rubbed bronze. You can definitely paint the old pulls, but make sure you prime them. A shiny nickel might not work well with the hinges/warm toned cabinets. If you try to change pulls, it's going to be tricky due to the angle they used in placement. You could try redrilling and wood putty that you stain, but I wouldn't go that route as I think it will be obvious. Be careful with measuring as some of the old cabinets can have non-standard pulls (learn from my mistakes). There are pulls out there in weird sizes, but it definitely limits your choices. Maybe something like this:
https://www.homedepot.com/p/Liberty-Essentials-Lombard-4-in-102mm-Center-to-Center-Warm-Chestnut-Drawer-Pull-10-Pack-P29613K-WCN-B/305756043
3. Ideally all the hardware should match. If you end up keeping the old light fixture then, you can pull it down and paint the metal portion the same color as the new pulls. You will be surprised at the difference on a light fixture. A new faucet with a sprayer would also be nice and not a huge investment in the same finish as the pulls/light fixture. I haven't used this formulation with the paint and primer before, but I like Krylon paint better than Rustoleum. Make sure to watch some videos about spray painting - it's definitely better to use a few light coats than one gloppy spray.
https://www.lowes.com/pd/Krylon-FUSION-ALL-IN-ONE-Gloss-Oil-Rubbed-Bronze-Metallic-Spray-Paint-Actual-Net-Contents-12-oz/1000876480
4. I would paint out the wood trim from the old bar area to try to make it disappear. It will make the space seem larger.
If you end up painting, here's a decorating blog I like with plenty of ideas about color choice for cabinets. There have been a couple of posts on here about painting kitchen cabinets and they would be a better resource for the best brand of stain or paint.
https://www.kylieminteriors.ca/painting-kitchen-cabinets-how-to-pick-the-best-paint-colour/
Happy decorating and congrats! Please let us know how it goes.