Just to get you started, you can get all the patches and mods you may want from here: http://www.nma-fallout.com/forum/dload.php
For Fallout 1 you should get the Children patch because GOG used the UK version which had the no children sensorship treatment.
For Fallout 2 I would recommend Killap's Unofficial patch. It fixxes some old bugs the developers left in there such as the Too Many Items bug. But others here will probably recommend the Restoration Project patch.
I also use the High Res patches for both even though I just upped the resolution to 800x600. You can use any resolution you want.
Check out the stickies at the top of the forum for all the recommendations.