The lower-end Ryzen CPUs will not release until later this year [strike]and they do not come with integrated graphics. [/strike]With your small budget an APU might be the best choice if you want to buy new. *I just saw about AMD Ryzen Raven Ridge APUs set to release later this year.
If you want to buy used, you could get better performance than AMD's current APUs. You could find a used pre-built tower with an i5-2400 and then buy a GTX 1050 or something similar to put in it. You may have to upgrade the power supply too, but all that should be within your budget.