DSLRs have the mirror that enable direct viewing through the lens without the need of a display (saves power) and have the AF system separated from the sensor. These autofocus systems are usually much faster if you need to track stuff.
Mirrorless can have electronic viewfinders and in either case the viewfinder or LCD will give you a preview of the exposure. The lack of a mirror saves cost (it needs to be aligned precisely) and space and enables smaller lenses, especially for wider angles. Phase detection sensors are needed for good autofocus and because mirrorless cameras with them have them on the sensor they can use them for focusing in video. They can also detect faces and focus on them automatically (some high end DSLRs can do the latter as well).
DSLRs usually have way more native lenses though most are designed for FF and the only FF DSLR below 500$ is from 2005. The lenses still work on crop sensors, but you get the center crop so FoV will be narrower and optical imperfections within the crop will be amplified. Mirrorless can technically use almost any lens with an adapter, but that means no AF and manual aperture settings in most cases. One Canon adapter can AF, but it is super slow and quite expensive.
Look at lens lineups and look for what you want. All of them have budget standard zooms and slow telephoto zooms, but some have various good values be it
ultrawide,
macro,
lowlight etc. etc.
I would look at that and see if I found a killer lens for what you want to do.
Just a curiosity, but one thing I don't know the full extent of is that mirrorless cameras with phase detection sensors seem to have ever so slightly worse low light performance. Take the A7R and D810, we should get similar ISO score from DXO with similar (identical?) sensors and we get 2746 and 2853 which are very similar. With the A7II and D750 though we get 2449 and 2956 and it's even worse (2248) for the A7 while the D600/D610 got the same 2900+ score. This is not a big difference, but I've found it interesting and I know phase detection steals some pixels that need to be interpolated.