What is your budget? Most DSLRs can capture sporting events, although some [much costlier] are better at it than others. The biggest factor in how well your photos turn out will most likely be the choice of lenses that you use. The "best lens" selection process will require some practice and experience.
Canon Field of View Comparison Tool
The best DSLRs choices, without going full blown professional, would be one of the "pro-sumer" models, like the 7D Mark II, or the 5D Mark III. I own a 6D, which seems to do an acceptable job with fast moving subjects, but does really well in low light circumstances.
Those two sports will most likely require two entirely different lenses, depending upon where you will be shooting from, and what part of the action that you wish to photograph. The biggest difference is that one is played outdoors, while the other is typically played indoors at the high school level. Because of the much smaller playing field, you will tend to be much closer to much of the action with basketball than what you would for baseball.
Each circumstance can demand very different lens requirements. However, there are enough similarities that exist that allow one, or two, lenses to be used for both sports. I would recommend one of the Rebel series cameras that come with 18-135mm lens. This zoom range falls into the category of "standard zoom", roughly 24-70mm, although it pushes the definition of "standard" range just a bit at both the top and bottom ends of its' zoom range.
The budget entry level Rebel camera models are not offered in a kit with the 18-135mm lens. The entry level models come with one or two lenses: 18-55mm on the short end; 55-250mm or 70-300mm on the long end. With the exception of the most expensive lenses in those ranges that Canon offers, the zoom lenses in those ranges are good for learning, but less than ideal for high performace. Most all of them are "slow", which means they have higher f/stop number ratings ... ... which means they have narrower apertures and require more ambient light to get good photos.
When it comes to shooting sports indoors, you will need a "fast" lens, which means a lens with a low f/number. Owning a zoom rated at a constant f/4, or even better at a constant f/2.8, will give you the best results indoors and outdoors. The choice of focal lengths will be highly dependent upon your shooting locaiton, location, location.
In addition to location, you may, or may not, want to use some sort of camera support, like a tripod or a highly mobile monopod, either of which can help give you sharper looking pictures because they help to minimize camera shake. Don't buy a plastic tripod from a big box store, because all that they do is best is "shake and break."
Before you make a significant investment in a lens, try to attend a few practice sessions and get a feel for how difficult it is to capture action photos, as well feeling out the focal lengths. A big zoom is not necessarily the best solution, because it takes a lot of practice and experience to use one effectively. You can always capture a shot at a lower zoom, and then crop the photo down to size a bit.
The 18-135mm range is a very good, all-purpose range for walking around and being a tourist. Another good standard zoom range is 24-105mm, which is another good range for being a tourist. The 70-200mm range is a very useful range to use when you want to close in on a specific subject, instead of capturing the wide angle sights and the big picture like a tourist. I cut my teeth on a 70-210mm f/2.8-4 lens, because it forced me to think about the shot just a bit, instead of capturing a wide angle, big picture.
The 70-200mm range may be a bit "too long" to use courtside at a basketball game, though. One of the extended range, standard zooms that I mentioned could work out well, but you may need a flash. You may not be able to use a flash, either.
The next zoom lens range from Canon is the 100-400mm range. This range of focal lengths would work well for capturing action around a baseball infield, as well as having enough reach to capture outfielders. Hopefully, you will be photographing baseball from a slightly elevated location, or at the field's edge near first or third base.
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