I'm going through the game again to try and get some better armor and I was wondering if drops were random? So can you get a really good piece of armor from a monster in the first level of the dungeon, or should I try and rush to a higher level like 8 if I want some good armor?
The drops are completely random, in that no two games will drop the same items. Actually the randomness is determined by your system clock, so if you get a program that lets you freeze your clock on a particular time, each time you enter say dlvl 1 it will have the same layout, same enemies and drop the same items.
But anyway, in answer to your questions about quality levels, the items dropped on dlvl 8 will be much better than those dropped on dlvl 1. Item drops are actually determined by the monsters you are fighting - harder monsters drop better items, and harder monsters are found in the deeper dungeon levels. This does allow for some variations, though. As you're aware, each monster comes in 4 different flavours ranging in difficulty, and the levels on which they spawn have overlapping ranges. So you frequently find different types of skeletons in the church for example, Skeletons and Skeleton Captains, and Burning Dead Skeletons and Burning Dead Skeleton Captains. In this case the quality of the item drops will be something like this (this is for illustration purposes, a guesstimate off the top of my head, so may be technically wrong, but purveys the idea): BD Skeleton Captain > Skeleton Captain > Burning Dead Skeleton > Skeleton. Basically the more difficult a monster is, the better items it will drop. So in the rest of the post I generalise about item drops in terms of dlvls, as generally the monsters that can be found on a particular dlvl have the same sort of difficulty, but on any specific level it is quite possible for some monsters to drop particular items that other monsters on that level simply aren't capable of dropping at all (Burning Dead Captain might be able to drop Studded Leather Armor, while a regular Burning Dead skeleton may only be able to drop Leather Armor as the best armor it could drop, yet both of these monsters might appear on dlvl 3).
There are two aspects to this - base items (large shield vs buckler, full helm vs skull cap, full plate mail vs rags), and magic affixes. Base items are linear, with the lowest items being found in the church, to the highest possible items being found in dlvl 14 (2nd level of Hell) onwards. So a skeleton in dlvl 1 might drop a cape or some rags, whereas a goat archer in dlvl 8 might drop ring mail or chain mail, and a cabalist in dlvl 14 might drop full plate mail.
The second aspect is magic affixes, where a wider pool is available from more difficult monsters, but the window is moving, so that the very highest level monsters cannot drop the very lowest affixes at all. So in the church (clvl 1-4) you might find a Ring of the Sky +1 to all attributes from a skeleton, but in Hell (dlvl 13-16) you couldn't find anything below a Ring of the Stars +9 to all attributes. Similarly, a goat archer in the cats (dlvl 5-8) might drop a Ring of the Moon, +5 to all attributes, but they could also still drop a Ring of the Stars, +1 to all attributes - what gets dropped is purely luck. So going into the catacombs will allow you to find much better magical affixes than in the church, but there's no gaurantee that you will do so. Going into Hell will definitely give you much better affixes than the church, due to the low-level cutoff, but there is still a wide variety in drops there also - you can find both Ring of the Stars +9 to all attributes, and Ring of the Zodiac +20 to all attributes, with Ring of the Stars being much more common.
Cursed magic items, eg those with negative stats like -% to hit, or -damage or -light radius, stop dropping about dlvl 4 or so. You certainly won't find any in the catacomb levels.
So for item finding purposes, as well as EXP and gold, if you've just started a new game in single player, it's worth rushing through the Church fairly quickly as the rewards down there aren't that great. The exception to this is if you're shrine-hunting, or looking for books as a sorcerer. Shrines can do things like +2 strength or +2 vitality, so can be quite useful even for high level characters. Spell books will help mages with their spell damage, although the church generally only has lower-level books like firebolt, charged bolt and perhaps lightning and firewall at the top end (these are still two very good spells however). The healing spell could also be quite useful for a warrior, however.
In multiplayer and in difficulty-bugged single player (see the bugs thread), the mlvl (monster level) of monsters in the entire game is bumped up a lot, which contributes to a lot of the damage (many formulas such as to-hit enemies, and chance to be hit by enemies, depend on monster level). The base item drops and gold amount drops are also determined by this mlvl. So what you find is that in Nightmare difficulty church, the monsters are dropping base items about equivalent to normal difficulty caves (chain mail and low-end plates) and gold piles are around 100-110 gold, however the magical affixes that they drop are still low-end (like "of the sky" vs "of the stars", or even cursed). In Hell difficulty, all monsters can drop all base items, but again those in the church and cats will still only drop the lower quality affixes.
Thus the best place, in terms of difficulty vs reward, to hunt for items is Normal Hell - they can drop all the top affixes, all the top base items, and it is much easier than NM or Hell difficulty. You only need to go to NM and Hell difficulty to find particular unique items from particular monsters, but more can be read about that on other threads in this forum.