To give a little background I have played UO since roughly 1999 but stopped on OSI right after Age of Shadows was released. Since then I have played exclusively on a couple different Renaissance era shards(Mainly Hybrid and Zenvera). Needless to say making the leap to not only a fully expanded version of the game but also one that has tons of custom content has left me in WAAAY over my head. ALL of this is new to me even though I have been playing UO for 16ish years. I have been here for going on 3 weeks and while I have acquired some weapons and feel that I have a decent grasp on those I am still wearing newbie armor because I have no idea where to even start on collecting decent armor... I can look around and see which items are popular as the "elite" eventual goal but I do not have the tens of mils needed to purchase all of those arties. I can find pieces that give me 100% LRC but then I have awful resists, the red vampire armor has great resists but has no LRC... The possibilities seem to be endless, much like this post, and I am starting to feel as if I am barely keeping my head above water with this stuff. I wish it were as simple as finding leather invul armor... Any and all guidance would be swell.

Welcome to the shard!  We do have a ton of content and options for gear.  First read the wiki, maybe join the new player guild for guidence and do most of the major quests for some great artys.  Next work on crafting to make a great weapon.  Take a look at the other top player gear and try and find those items over time. 

Also on a somewhat related note, is the dragon cloak only available as a bonus for a $200 donation? I see it listed on the web page as one of the items to choose from when you donate that amount but don't see it listed anywhere else for a set amount of ED.
Every item can be found, crafted, bought at auction or from players...the donation option just gets you there quicker and supports the shard.  The Dragon Cloak can be crafted in game, see the display and info on the wiki

Unfortunately, there is no easy answer to your question, but here goes:

I never used the apprentice gear. My first order of business (on any server) is to gm tailoring and build me a 70 physical leather suit. I then hit demise up and start grinding out ettins and earth elementals like a boss. Sounds cheesy, but those dungeons exist for reasons like this. Expo ( I think it was him) even remodeled the dungeon to make it look good, and there's an ettin slayer quest that can be picked up at the entrance to make your time there more profitable.

After getting some gold built up, I'd start by either buying peices of armor from vendors (not too bad if purchased one piece at a time) or my favorite method, would just be to find a blacksmith in game and have them whip you up a suit. Its not a popular choice but most people reserve platinum hammers for weapon creation and consider the lesser hammers to be near useless. Explaining that you are new and that gold is limited to you, would probably net you a cheap if not free toxic runic armor set. Just try saying this in game from time to time. [trade New Player Looking for Runic Armor

You'll be amazed at the results.

From there I'd find me either a Zelda sword or a nice dragon slayer weapon and hit destard. Gold will not fall from the heavens at this point, but you'll find that you'll have enough to get what you need. As for the rest I'll leave that up to you. Here's a few tips though.

You have unlimited skills, use them.

Spirit Speak is potent at 100 skill- use it to augment your healing, so is the Chivalry spell Close wounds. Close wounds is based off your karma, not skill, so it will be a beast of a healing spell early on and doesn't require spell channeling to work.

People sell orange petals, buy them. Immunity to lesser, magical poison is nothing to laugh at.

Bard abilities. These are extremely powerful. Against a single monster you can peace it then discord it, making it damn near simple to beat. If a second interloper joins in just provoke it and you're good to go.

Gems. Make sure you are looting these. If a dragon drops 800 gold and 4 diamonds and you leave the diamonds behind, you just lost 400 gold.

Vampire Form is king in pvm if you need life leech. If you need mana then Wraith Form. When I pvm I always have one of these forms active. There is no reason you can't actively switch between the 2 even mid fight.

After you get semi geared up (getting the items you want isn't that hard, wait til you start getting them socketed) you'll find new methods of getting rich. At which point I'll leave the means and methods up to you. Oh and the dragon cloak can be crafted though one of the ingredients is on a ridiculously long timer. It's a fairly end game piece, so unless you are preparing to donate for one, I'd just rock something else until then. It also has to be leveled up once crafted and the dragons that need to be slain are bordering the ridiculous in difficulty. They can be solo'd fairly easily but the tactics involved are not in the realm of new player capabilities. So I'd hold off on that one for now.

Then again, you could always join a guild and beat them as a group. Have fun! Hope this helps.

A good intermidiate set of armor like the astro deamon set, combined with fortune armor and cloting can meet all your requirement, resists, lrc and lots of added stats and luck.