Hi and welcome to the forum:
An actual budget figure would really be a big help, but given the camera you have is an old unit and a modest model, I think you might want to consider the following two pairs of lenses: in each option one for general walking about, and one for more distant subjects. Much depends on the lighting conditions, and how close you will be to the action. Here are a couple of options though:
Option A:
Canon EF-S 18-55 IS STM: this is the best version of the basic lens that comes with most cameras like yours. It is a good lens, silent, fast focus. It is the cheapest, smallest and lightest of the optics. It is limited in what it will show - i.e. it doesn't show detail of far off objects, which is why a second optic would be best for sports etc.
For more distant subjects:
EF-S 55-250 IS STM - the cheapest additional optic, good performer. It extends your optical 'reach' and is again small, light and very economical.
Option B:
Canon EF-S 18-135 IS USM. It is an excellent walk-around, general-purpose lens that is light, extremely fast to focus, has good optics, also great for some close-in sports, and portraiture. It offers more significantly reach that the 18-55 unit in option one and is within your $400 budget. It might work for you on its own or at least give you more time to consider a longer lens.
For more distant subjects like motocross, etc. where you can't get too close to the action, the following will give you more detail.
Canon EF 70-300 IS USM f/4-5.6 MkII - see this article 70-300 Canon Lenses In-Depth Analysis - Canon Community
or...
Sigma 100-400mm f/5-6.3 DG Contemporary for Canon this will offer the most reach for distant subjects like motorsports, but is likely to be more expensive. Note that with any 3rd-pary lens, you must specify it is for Canon EF as they make the same optic for different companies.
If you are in the US, you might want to look at KEH.COM, which sells used gear of quality and backs it with a warranty - they are highly regarded. Canon used to sell EF-S lenses but seem to have stopped that now as they move to a different platform
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
