Ok my 2 cents :
1. is always good to have 2 sets of amor, when fully upgrade you can change the name, usuallly i go with dps or tower and then type ei plate, leather and such so that i can find them easy when swaping. the gear is always clasiffied by class ei head, chest, hands but not by type when is in the inv box, being pets always first, weapons by hero class then armors head, chest gloves and boots. i only keep the good stuff lock and anything i want to keep but not use is usually drop in the tavern (locked tavern that is) to save room for items as you have only like 13-14 pages you can store. tavern drops caps at 85 i think, not sure thought. you can have a set you like drop on top of a table in the tavern as your dps set and before changing drop your current one on another table before picking it up with the triangle (square, takes it to the inv box).
2. drops at the end of battle as reffering to rewards (boss, map completion, challenges) yes supposebly the higher the difficulty the higher tha chances of higher upgrades gear to be rewarded (upgrade = this symbol in the forums ^) i have heard of people of getting higher ^ weapons from medium and hard than insane, insane + (even on easy) is all about luck.
3. the higher the difficulty of the map (hard, insane, insane+) the better chances of having high ^ ARMOR from tavern shop. keep in mind these refers to when you complete a map on lets say insane+, that is a higher chance of a 80-100^ armor to appear. weapons i'll say 99% of use prefer from DLC's like morrago and aquanos than the tavern shop. (depends on your game progress) exception to this is the sould focuser which i think we all farm from alch lab insane, insane+. what makes this weapon the exception is that shoots through walls and can reach 100+^ with lots of luck. tavern shops reset after each sucessfull completion of a map or challenge.
4. for game progress i'll say you can literaly run until you reach ramps and farm ramps chest on hard for armor. weapons is more specific. a good weapon can be found anywhere as you go. past level 70 you want to farm specific ones. is all base of status of your current one, and again number of ^ and weapon status ei tower stats or dps stats. 95 % of the times chest drops are way better that mob drops at your level. level 70+ mob drops are always auto sold and i only check chests. (at level 70 you can run glitter hard for even better armor pieces, my first godly's/legendary sets where from here with >30^ for level 70, but was getting gear up to level 90 with 80^ that i saved for later, ran it like 50+ times to get to 74 btw)
5.score has nothing to do with items, score is xp gained during that map. there is bonus 30% more exp at the end of battle if you accomplish one of these specific requirements : 30% if crystal does not get hit, 30% more if hero does not get hit, 30% more if hero only uses weapons (did not spawn any tower during all the map) so glitter hard missing all these is around 400-500k exp while performing all these is 800-900k exp. quite a difference is it? glitter insane yields 2.2-2.5million exp with all 3 bonus.
6. boss, challenges and map completion rewards are base of the hero and is the same every time for that hero, rewards is based of the difficulty also. boss and map completion is one per hero at completion of map but rewards is one per profile. huntress reward for alch lab on insane/+ is soul focuser but on hard < is something else you can google dungeon defenders wiki and search for maps and it will tell you rewards per hero and every thing you need to know about it so that you can get specific weapons. keep in mind that this page is for PC mostly, has info on ps3/xbox but item pictures are usually for pc which can reach status not available for console ei ultimate gear and such (this will never come to console)
some other tips.
before buying exp bonus from tavern set any map to insane+ (you dont have to run the map just set the difficulty to such) and you will get more exp than if the map was set for hard.
if you like like to know some more about starting progress read my response this. it is a small diary of what i did and some tips.
if you got questions ask, we like to share our knowledge. http://forums.trendyent.com/showthread.php?94213-Newbe
btw sorry for the gramatical erros I'm at work now and really sleepy.
Hope this helps and welcome to our community.
+1 For Helpfulness.