Well they sell them as creative suite now and it is $20 a month for a single app. Also, they have a deal where you can get photoshop and lightroom for $10 a month. But if you are a student you can get the whole creative suite which includes both Photoshop and illustrator for only $20 a month (regularly $50). You would also get a ton of other apps, including adobe premiere pro for video editing. So if you are a student and want the creative cloud you could get both.
If you don't like the per month option you would have to buy the older versions online somewhere. If you want something really cheap you could get photoshop elements 13 for $100 but since they just came out with elements 13 you could probably find elements 12 online for $50 or less. Elements is like photoshop but it doesn't have as many features, but if you are just starting out I don't know if you will need all the features.
Photoshop and Illustrator are two different programs. Illustrator is more for vector graphics which is good for designing logos and such. But Photoshop would be the one you would want. Most YouTubers use Photoshop or a similar program for their thumbnails rather than illustrator.