Just on a whim when making my character I was thinking of going with 1 luck and I was trying to figure out what it would affect other than critical hits. After reading it seems to affect the chances of random encounters and likely special encounters as well.

Anything else? I'm so going with this just to see how far I can get but if I manage to go along I would like to be prepared in case it could affect character interaction and the main mission.

There's a guide which recommends playing a character with 1 luck so shouldn't be too painful.

Combat versus heavily armored high HP foes like wanamingos will be a little harder without the better criticals cheese (but aiming at the eyes should still be very effective) and critical misses will have a slightly higher chance to be worse than just normal misses.

I would say not to worry about the critical hits, but the critical failures. The list of critical failures includes such wonderful events as accidentally shooting yourself, dropping your weapon, somehow losing all the ammo in your weapon, losing a turn and (my personal favorite) having your weapon explode in your hand causing more damage to you than anyone else. If you want to go this route I would suggest an unarmed character as there is less that can go wrong. I once played an unarmed specialist with the Jinxed trait and it was kinda fun as everyone else had the misfires and exploding weapons. The worst thing that happened to me was trying to kick someone in the eye and breaking my leg instead.

The critical miss roll is affected by your chance to hit so if you have 95 percent hit chance the critical misses shouldn't be too bad. If you attack with only 5% hit chance on the other hand it can get very dangerous.

I've never tried a character with 1 Luck, but it seems like it would be much more suited to a melee character than a shooter of any kind. For one thing, the Sniper perk requires a successful Luck roll for each hit to become a critical. On the other hand, the Slayer perk makes every melee hit a critical without requiring a Luck roll, so in the long run, a melee character should be able to overcome it and thrive.

Good to know, I'll make sure to only attack when I've a high chance to hit then. Interesting. Are there many different melee weapons in this game? I might go for that with 1 luck in case there are.

Yep. Effective ones as well. Unarmed combat is also a viable option.
Just put enough points into agility to get a decent amount of action points.

And maybe also points into energy weapons once those start popping up.

Technically you'll always be weaker than a luckier character due mainly to the decrease in critical hit chance. This will affect all players to some degree, but it's nothing you can't compensate for.

I played one game on very low luck (but not that low), and the differences in combats compared to my run before that where I had luck at 6 was definitely noticeable. Ranged characters both times. I think the biggest difference is due to not being able to pick up Better Criticals, More Criticals or Bonus Ranged Damage. That and the Sniper perk, though obtainable, is useless without high luck.

So ranged characters are definitely disadvantaged more, plus critical failures tend to be deadlier with ranged weapons; however, the lack of better criticals will have a noticeable effect for all characters. Of course, the Slayer perk makes up for that somewhat.

There are other perks you'll miss out on, but they're probably not ones you've even thought about taking anyway.

There are some good weapons, you can easily mix it up with anyone using ranged weapons only - provided you close the gap first. Melee weapons also tend to be faster to use than ranged weapons, with unarmed being faster still (for the punch anyway, which includes power fist and brass knuckles).

Since you can get lots of free unarmed training, I'd go melee first, then unarmed - though it can be tempting to drop points into unarmed just to unlock all the extra combat moves. Weapon details are on this wiki: http://fallout.wikia.com/wiki/Fallout_2_weapons

One more thing - I think while low luck will decrease your chance for most special encounters, I think it increases your chance of getting bad ones - at least the "special" bad ones. Do you like dogs? ;)

Yes, and as Jarmo said unarmed works too, and as you pump points into it you get more fancy moves.

Melee has the Ripper and the Super Sledge and a bunch of others, but Brass Knuckles and the Power Fist count as unarmed. Slayer works for both melee and unarmed. For a melee/unarmed character your priority is going to be having lots of action points for movement, because you need to be able to cover lots of ground.

If you try it with 1 Luck, you're definitely going to want to shoot for the Slayer perk, I'd say. Plan ahead to get it ASAP.