If you are shooting these games at night, you’re going to have trouble with a F/3.5-4.5 lens. It just won’t collect enough light for any kind of action shots under field lights. The D60 isn’t really know for its low light ability.
If the games are during the day, that 10-24mm F/3.5-4.5 will probably work fine for you.
If you don’t want to spend a lot of money on a wide lens, look at the Tokina Lenses. Tokina has a 11-20mm F/2.8DX lens for Nikon that probably does decent in low light conditions.
I have a Tokina 16-28mm F/2.8 lens this is glued to my Canon 6D(full frame camera). It is very crisp. I run a bunch of different zooms on my Canon 80D(APS-C crop sensor), but I use the 18-135mm F/3.5-5.6 as my “walk around lens”
If you are interested in learning, looking up Tony and Chelsea Northrup on YouTube.
Agree with everything you said, especially that it is not the best for low light shooting.
Also the 10mp sensor is more than adequate but some of the newer inexpensive models have more pixels without sacrficing speed.
Some of the more expensive models have ridiculous ISO but if you get to the very high ones you sacrifice some quality.
I would look at Adorama or B&H used dept and get another body before getting another lens. I would not go below an excellent condition rating unless the price was really low. They do describe them fairly.
They are not the same quality as Nikon but I have had really good luck with Tamron, Tokina and Sigma lenses.