I've got a canon point and shoot that takes awesome macros (for what it is), I've got another (newer) model that is meh.... not so hot
Ditto on Nikon, I had and older one (got dropped LOL) that took excellent macros (again, for what it was) replaced with a newer model that sort of sucked.
Much good advice from some very intelligent people... as you see, it's a passionate subject.
Like stated above, I've got Macro and Zoom lenses that cost more than your entire budget... good glass isn't cheap.
However, you can do well with a good prime lens and extension tube or a nice cult lens... but you got to do your homework.
If you think you might like cult lenses, Canon does have an advantage, more lens formats can be adapted.
Recently "mirrorless" cameras have become the rage, but I like a viewfinder... many times the LED screen is unusable due to ambient conditions.
I'm primarily a Canon owner... in your budget I would probably go this route before I bought a point and click:
http://www.bhphotovideo.com/c/product/827671-REF/Canon_5157B015AA_EOS_Rebel_T3_Digital.html
Its a versatile
entry level refurbished DSLR.... its a start
Caveat, that is based on my bias toward canon glass and vintage lens use