You need to think more than just a camera. All you will see is a load of figures with hoodies up or caps pulled down low meaning you cant identify them.

Plenty of hires outdoor wildlife cameras for that price range that will do what you want.

You also want to be thinking flood lights etc to help deter them. Preferably something likely to get your attention if it comes on while your awake.

Maybe even a decent alarm, sensor on door, sensors on back gate etc. IR beam as long as its above pet hieght can be useful. All set up as a zone on the house alarm so you can set it once in the house.