You might struggle with a remote trigger I think on bridge cameras. Just use a tripod & 2 secs self timer.
As for which…I am not sure. How much detail do you need? The min focus distance can vary a lot, although with high mega pixels you can often just crop in anyway.
My Nikon P300 does pretty good in macro mode, but I suspect it will be similar to the equivalent Canon, Panasonic etc.
One thing you should get is some kind of exposure compensation/manual mode as close ups of things like engineering detail often trick the camera into over or under-exposing the bit that is relevant to you.