Ok, so that power supply is decent enough. Not great, but not bad either really. It is however probably around five years old so the warranty has likely either expired or soon will. That could be a concern for you and is something you should consider replacing before too long. I never trust a power supply that is older than the warranty on the device, with brand new hardware. If the manufacturer felt that was the length of time they were willing to trust the device to last, safely, then that is how long "I" am willing to trust the device to be reliable for when it comes to using it with new and expensive hardware.
Using it with older hardware that has already outlived it's primary usefulness is a different story. I'm a little more forgiving there because I'm not going to be as heartbroken if an old power supply takes out a five year old motherboard or graphics card as I am if it ruins my brand new hardware. So I'd think about that as well.
Assuming it is fit, it is good enough for any of these cards we are talking about.
I think the 1660 ti is the best fit and safest bet right now. It has about 5-10 fps higher on the 1%/minimum frame rates over the 1660 Super. Considering it is only about fifteen bucks more expensive and that those five to ten FPS might be enough to make a difference in some cases since the minimum FPS is where we normally see the most hiccups and problems at, it's probably worth it. I'd recommend this card as the least expensive option that is still a superior product, in that card family.
PCPartPicker Part List
Video Card: EVGA GeForce GTX 1660 Ti 6 GB SC ULTRA GAMING Video Card ($243.98 @ Newegg)
Total: $243.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-02-25 22:05 EST-0500
If saving a few bucks is more important and you like the idea of the Super instead, then this would be a good choice.
PCPartPicker Part List
Video Card: EVGA GeForce GTX 1660 SUPER 6 GB SC ULTRA GAMING Video Card ($228.98 @ Newegg)
Total: $228.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-02-25 22:03 EST-0500
Or if you want to spend a few bucks more and get a significantly better product, then I'd recommend this:
PCPartPicker Part List
Video Card: EVGA GeForce GTX 1660 Ti 6 GB XC ULTRA GAMING Video Card ($312.49 @ Amazon)
Total: $312.49
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-02-25 22:08 EST-0500
If any of those show up as not currently available, wait a day or two, they'll be back in stock again. Obviously there are some other choices as well from ASUS, MSI, Gigabyte, etc., but IMO if you are going to buy an Nvidia based card, EVGA is who you buy it from. Same as if you are going to buy an AMD based card, your first look should be at whatever Sapphire has to offer and then possibly look at XFX reviews as they are often a close second but sometimes have some real issues with some of their card models.
For Nvidia though, I try to stick to EVGA, then the rest including Zotac or Palit who also make very good cards but nobody is on the same level as EVGA when it comes to customer service after the sale and with graphics cards, that is something you should be very aware of because the chances of needing to use it are much higher than for other hardware.
All of those cards listed above are more than capable of giving good 1080p performance.