What's that about a time limit?
You'll have 150 game days to complete the first main quest in the game, which is finding the water chip for Vault 13. There is a way to increase that time limit by 100 days during the course of the game.
Also, in Fallout version 1.0, you have a secondary time limit of 500 days to beat the entire game, or 400 total if you extend the first quest by 100 days. However, in version 1.1, these two total time limits are removed--another good reason to upgrade. After you find the water chip, you'll have approximately 13 years to finish.
So does that mean I have to rush to get the water chip?
Not at all. 150 days of game time is actually well over enough, even if you want to finish all the quests until that point. In fact, you don't actually need to find the water chip at all if you solve the two subsequent quests before your water chip time limit expires. Of course, you won't know what they are your first time through without thorough exploration.
Bringing up your Pipboy 2000 tells you exactly how many days you have remaining. The only concern you may have is if you find you're running low on time due to wandering around the map too much. How much is too much? Exploring the entire map is too much, but certainly exploring 1/3 to half of it should be okay. Simply keep an eye on your Pipboy 2k from time to time, and you should have plenty of time. If it ever gets to about 30 days remaining, begin thinking about doing the necessary quests to either extend the time limit another 100 days or finding the chip. You can explore virtually forever after you return the chip.
How do I give my NPC's weapons and armor?
You can give them anything you own, but they'll eventually run out of space. NPC's won't wear armor that you give to them (yet in Fallout 2 they will), but it doesn't mean you shouldn't load them up like a mule when possible, due to your own carry limit. Simply hit the number 3 key for the "Steal" skill, click on the NPC, and you can freely give and take items from your respective inventories, without penalty. Perhaps they didn't have the time to come up with a way to do this normally, yet stealing from them is the universal method of dealing with their inventory. Ask them what types of weapons they are proficient with, and give them a weapon of that type. To make them switch to the better weapon, simply talk to them and ask that they use their best weapon during combat, and they'll likely put away whatever they were using prior.
What are some good combat tactics?
Against other melee attackers, especially at the beginning, attack only once and use your remaining action points to run away. The critter will follow and hopefully will not have enough action points of its own to attack. When it's your turn again, attack and run, and repeat until the enemy is dead. Works well on smaller animals especially... like rats, scorpions, etc., and when you have a higher agility.
Another good one is to begin making targeted shots once your skill is decent, and aim for the eyes (or ganglia or sensors... or whatever the enemy has in its "eye" spot). What's a decent skill? If you're attacking from a range, then 90% or higher is about when you can make some decent targeted shots. If they're within melee range, you can make targeted shots slightly sooner with some degree of accuracy. Targeted shots increase the chance of a critical hit, which always do more damage.
Against fallen enemies, you can use targeted shots with an increased chance to hit. Try shooting male characters in the groin so they fall down, or anyone in the legs. Then use a targeted shot in the eye to finish them off after they've fallen.
With all of the different types of ammo, how do I decide which to use?
In general, the weapon you decide to use makes that choice for you. Look at its description in your inventory. In some cases, you'll acquire both JHP (jacketed hollow-points) or AP (armor piercing) of the same ammunition type, like with the 10mm JHP, or 10mm AP. The armor piercing (AP) ammo in this game supposedly does not work as intended, so I'd advise sticking with the JHP in those cases where you can use both.
Is there enough ammo to go around?
In the very beginning, conserve just slightly. Later, you'll have more than you know what to do with, of almost any type. There are a few exceptions, like the rare 9mm Ball... or BB's. Since the weapons that use this type of ammo are generally more like novelty items, you shouldn't be worried about a lack of ammo in this game. Fortunately, many of the enemies you kill will have enough to keep you filled.
What's the maximum level and where will I likely be when I finish?
You can level up to 21, and you'll likely be anywhere from 16 to 18 when you finish, if you complete most of the quests. You can always look for random encounters, some of which give a substantial amount each time, and level up even further.
Where is the best place to level up?
Spoilers! I can't imagine that you want to be spoiled being that this is a complete walkthrough.... but I thought I'd warn you just in case. There are three main places to level up in the game. The place with the most xp for the least amount of time is easily in the Boneyard, Warehouse area. There are two or three deathclaws that respawn after an hour if you leave and re-enter the map. Each of them give 1000xp. Apart from that, many people like randomly wandering near the Military Base for the increased mutant encounters, which give 1500xp on up generally, but you must be extremely powerful at that point. Thirdly, there is the safer steady route. You can join the Crimson Caravan in The Hub with a great chance of combat. It is also a good way to pick up more stimpaks (though you probably won't need them).