Ian Steadman has written most of what you need to know regarding the standard modifications:
http://www.ianstedman.co.uk/Amiga/amiga_hacks/A1200_Mobo_fix/a1200_mobo_fix.htmlGenerally, you'll only need to apply certain modifications to fix compatibility with certain expansions.
Yes, you should replace the electrolytic capacitors in it. And yes, you should always test it first before you mess around with it in any way.
The power supply is subject to the same ageing as everything else, so unless you've kept it in your DeLorean for the last 25 years, you might like to replace the components that suffer age related problems. i.e. replace the electrolytics in that too.