Tilt/shift would be best for getting a wall or somesuch flat plane in focus. But the lesne will probably be more than your budget, and if you’re new to cameras then contorling a tilt shift lense won’t be the easiest skill to learn at the same time!
Indoors there’s low light, so you’re going to want good lenses. But to get the whole room in focus and be usefull for zooming in on any damage then you’d want to stop the lense down which further limits light. Compact cameras with smaller sensors tend to give much deeper depths of field so the whole room can be in focus.
Then there’s the problem that images straight out the camera often don’t look very ‘expensive’, all the sharpening, colour saturation and generaly making them look good is added later in photoshop/lightroom etc, which kinda ruins their validity as ‘evidence’. Whereas compact cameras usualy do all that for you in camera (that’s what the mode dial on top is for, it makes a reasnoble set of guesses for the settings based on what you tell it you’re doing, i.e. indoors).
Basicly if you use a DSLR like you would a compact, the results will on average probably look worse than they would have with a good compact. With the added dissadvantage that the DSLR result will very more with your skill/luck each shot, and the compact will always produce the same consistent quality of results.
If you do go down the SLR route, my money went on Pentax K-5 (k-5ii should be under budget now) as the manual functions are much easier to access than anyting similar from Canon/Nikkon so functionaly it’s closer to their Pro cameras even if the internals are the same tier as the direct competition, that and the magnesium body and weatherproofing.