The recommendation below is an advertisement. Most of the links here are part of Amazon's affiliate program (unless otherwise stated), which helps support this website. It's also more than that - it's a hand-picked recommendation of something I've used myself. If you're interested, here is a full list
There are a lot of options for illustration software out there, but mine has always been Adobe Photoshop. I've been using it for nearly 20 years now, ever since I started fooling around with digital art, and it has served me well into my career, both in freelancing and in studio positions. One of the biggest advantages, in my opinion, for those jumping into digital art with Photoshop now is its accessibility. Where when I was younger, it'd cost hundreds, even over a thousand dollars for a software license, younger students can now get their feet wet with industry standard software for just $10/month with their Photography Plan.