What equipment do you give your characters?
The best possible equipment.
Seriously, though, I tend to have my warrior classes decked out in the best armor available with shields and long swords. Rarely, I might go with a two-handed sword. My mages will typically have darts and a quarterstaff (but only for when enemies get too close).
What do you do when your party is battling an army of pesky goblins?
Or how about those annoying monsters who are immune to non-magical weapons or spells?
If I have the weapons or spells to deal with them, I do. If not, I flee the battle and tend to make a note that when I review the module to mention that the author didn't provide me with weapons I needed to defeat the encounter or set it up so that I would be the appropriate level before reaching it.
How do you protect your less defensive players such as mages?
Whenever possible, make sure the warriors and heavily armored classes (like the cleric) are in front of them to cut off access to the enemies.
I've heard about having characters who use bows and arrows in long range, then when the enemies get close enough having them switch to swords and fight like that.
Also a decent strategy, but one of the failings of 1st Edition AD&D is that bows don't allow you to add any bonuses based on your Dexterity or Strength scores (something that later editions, I feel, did better). As a result of that, it's better to just close the gap and start hitting things with weapons.
In addition, getting into melee with your enemies can prevent them from using ranged weapons against your vulnerable party members (like mages). So, most of the time, I don't bother with arrows.