Hello lost_lemming, welcome to the EAB - I hope you enjoy your stay.
Yes, probably the biggest issue that comes up when recommissioning an Amiga is 'how in the hell do I get any output?'
For simplicity's sake:
No modern monitor can scan low enough to display the Amiga's output. (slight lie)
So...
-Use the TV-out (horrid)
-Pick up an old-style monitor - C= ones obviosuly, but an old multisync or Acorn monitor will do. (you'll need a Amiga-15pin adaptor)
-VGA-Scart lead to a TV / monitor that has such an input (not bad, some TV's don't like Amiga SCART leads)
-fleaBay has lots of 'av-mixer' boxes that can sort out the signals for you. Ask for advice here before you buy.
-Scan-doublers/flicker-fixers are available (just) - internal & external. These up the Amiga's output to a range modern monitors can lock onto.
-Buy an Indivision. Not cheap, but by far the best output & available new.
Then you get into home-brew projects if you feel like a little soldering...
-S-Video out hack. Good if not the best quality (I bought mine from a fellow forum member)
-There's also a recent thread about an all-singing-and-dancing external upgrade
I hope the above is a useful start to you plans.
Regards,