Fallout 1 is good to go, as long as you have the latest official version which is 1.1. Other mods can be added to your taste, but the game is perfectly playable.
The official version of Fallout 2 is broken as hell. It has hundreds, maybe thousands of glitches that were never fixed by Interplay, even with their patches. This is probably due to much of the game's content being cut before it was even completed. Thanks to Killap, however, this is no longer a problem. He has created a massive patch that took a couple of years to finish. It fixes the published game. He has also created the "Fallout 2 Restoration Project". This is an endeavor by Killap and others to restore all the aforemention cut/incomplete content, which was still crammed into the game's code. It adds many quests and new locations to the wasteland.
You can find both of these
HERE.
To use either you should have the latest official version of FO2, version 1.02, which you probably do. Then use either the patch OR the FO2RP, not both. The patch is incorporated into the RP. There is one minor thing worth noting about the FO2RP. The content that they wanted to restore is complete. But, there are a few minor bugs left in the RP and Killap is working when he can to squash them.
None of these bugs are game breaking, however. The next update will likely be the final one for the full English language version. The only update planned after that will be putting multilingual support back into the game.
Once again, other mods can be added to your taste, but either Killap's patch or the Restoration Project will give you a complete, playable FO2 game.