The term "compact DSLR" is not a standard one. Maybe you are thinking of
full frame (35mm film equivalent size) versus
"half frame / cropped sensor / APSC / micro four thirds (all ~~~= 1/2 of full frame).
Or mirrorless with ~~= APSC sensor or ...
The main features which put cameras in the "serious" category are,
a sensor at least 1/3 of full frame size or more (somebody will cite something slightly smaller)
and interchangeable lenses.
Anything else is mass-market or niche. You can get some very good units of both but assume you want a large sensor camera with removable lens.
The good news: If you buy towards the top end of your budget then essentially anything you buy will be an excellent camera. Nothing in that range is perfect (and no camera really is) and features and performance are not top top class, but still objects and clarity are "bread and butter" to any serious camera.
You need to be more specific, to allow people to zero in on what may suit you best. This is close to a shopping question which is frowned on BUT if you can be specific about your main applications(s) there may be good targeted advice.
As a rule, if it's labelled Nikon, Canon, Sony, Pentax, Olympus, Fuji*, and a few more you won't go too far wrong. Read good reviews and ask specific questions.
(* an interesting trend in source of brands, no?)(There are others that don't fully follow that trend, but not on your budget. Leica, Zeiss, ...)