The EOS 60D is a good camera for its era - I had 3 of them! If you want to stick to that body, I would suspect that the camera originally came with one of the following:
EF-S 18-135 IS lens,
EF-S 18-55, and possibly a EF-S 55-250 IS USM or less likely EF 75-300 USM
For sports at night you would want something at least in the 70-200mm range, and for your budget I would recommend the EF 70-200MkII L f/2.8 or f/4 IS USM lenses. These are lenses with a large aperture and thus let in a lot of light that will compensate for the lower light performance of the older, smaller APS-C sensor. They have excellent image stabilization and while heavy (they are all metal) are pro-grade lenses and can be used with a monopod.
However, another thing to consider is the age of the camera itself. They, like us, have limited life-spans and this is a 14 year-old model. So, for the same budget I am going to offer a devil's advocate proposal of changing the camera and lens for one of the new Mirrorless Interchangeable Lens Cameras (MILCs). Normally, I would say that even if the camera is older, as long as it works for your purposes it is still valid, but the new MILC cameras offer advanced features that will definitely offer benefits both for low light and for getting sharp images of the sports.
Sensor technology has come a long way in 14 years, and the new cameras offer much better performance in low light (better dynamic range), and have massively improved focus, with the ability to find face and eyes, and track them as they move - that is absolute gold for anything involving getting sharp images of animals and people - especially in sports. Finally, what one sees through the viewfinder shows how bright or dark the final image will be, which a camera like the 60D could not, so one is much more likely to be able to achieve the right exposure.
I would suggest considering a camera and lens from the Canon refurbished site. These are often unused but surplus stock, open box but not used, display model or demo model. They are fully-functional, serviced and come with the Canon warranty. So, 'good as' new, if not actually new. There are savings to be made here that will help.
I am going to base my suggestion on two principles.
1. Indoor sports demand low light performance and larger full-frame sensors (the 60D has a smaller APS-C 'crop' one) gather more light across the larger sensor area, and thus perform better in those conditions. They show less noise, offer better colour and tonal values, and can be used at much higher ISO (sensitivity) levels.
2. You likely don't want to be changing lenses in the middle of a game as the players move up and down the court, and thus change the focal range from wide to telephoto as they move from close to far. So, a single lens with a wide focal range would be advantageous.
I am thus going to suggest the Canon EOS R8, a full-frame camera, with a large 24MP sensor, face and eye tracking, great ISO performance, and with lots of options to customize controls for various scenarios. Right now they are out of stock at the refurb site, but if you follow this link you can get notified when they are available. Refurbished EOS R8 Body (canon.com).
For real-world reviews:
Canon EOS R8 "6 Months Later" REVIEW: Best Budget Full Frame Mirrorless Camera?! (youtube.com)
Canon EOS R8 REVIEW vs R6 II: best value full frame camera? (youtube.com)
As to the lens, you need an RF lens to work with the full-frame R body (your old lenses will not work well with an R series FF camera): to get the flexibility, I would suggest:
Shop Canon Refurbished RF24-240mm F4-6.3 IS USM | Canon U.S.A., Inc.
This lens has a fantastic range, image stabilization to make hand-holding easier and is not massively heavy.
For real-world reviews:
Canon RF 24-240mm review SUPER-ZOOM for EOS R! (youtube.com)
The most underrated Canon lens! (photo/video samples) (youtube.com)
Like any device, one gets the most out of a camera by studying the controls, so here is a link to a tutorial on the R8:
Canon R8 Tutorial Training Video Overview Users Guide Set Up - Made for Beginners (youtube.com)
A note on lens corrections:
Before the impact of Computational Photography, which has made cell phones produce great images, lens makers had to use pure optics to get a great images with better focus, distortion and diffraction control. This made them both extremely heavy and very, very expensive.
Computational Photography has now come to modern dedicated camera optics. That means that the pure optics alone are now combined with digital algorithms to make corrections to the digital image and produce brilliant results at a much lower price and weight.
How this is done is that the lens actually shoots a little wider than the advertised focal range, by about 3mm. That 3mm wider view is used by the algorithms to make corrections and render a beautiful, corrected image at the advertised focal length. This is done automatically in-camera for looking through the viewfinder or saving JPGs and, if you shoot in RAW mode post-production software automatically corrects the files as they are loaded. This new approach is not limited to these non-pro lenses, it is also used with them - I have the RF 14-35mmL f/4 professional lens and it does exactly the same thing. It's just dedicated photography catching up with advances cell phones have had for a while.
I enclose some images I have taken in different conditions with the 24-240 and the EOS R6 (which has an earlier 20MP FF sensor):
Moody Morning the the R6 & RF 24-240 - Canon Community
The second link is with the same lens and the more demanding 45MP EOS R5 that will show any flaws in the gear or technique:
Trying out the RF 24-240 on Wildlife with the R5 - Page 2 - Canon Community
cheers, TREVOR
The mark of good photographer is less what they hold in their hand, it's more what they hold in their head;
"All the variety, all the charm, all the beauty of life is made up of light and shadow", Leo Tolstoy;
"Skill in photography is acquired by practice and not by purchase" Percy W. Harris
