Armor:
Startup levels: Med Suit just like any other profession.
Levels 30-70: Carbonum Plate Armor is a solid option, adds NCU and Nanopool both things is good to have plenty of. Also consider the modified versions Omni Carbonum Plate and Storm Carbonum Plate for Clan players. Junkmetal isnt a bad choice either.
Levels 70-110: Prowler Armor or the more expensive Predator Armor is good choices, however if you lack the funding, go with a new set of Carbonum/Junkmetal. Before level 100, get your OT Standard Executive Secretary Suit/Standard Clans Administration Suit From the Foremans Office (guide on how to make the Suits can be found at Anarchy Arcanum). With a QL300 City the suit can be equipped around Level 20. Other options for a back item is Neleb's Nano-circuit Robe, Reanimator's Cloak, do NOT use a Albrecht Heavy Tank Armor as these gives you +Nanocost, only the QL200 Albrecht Heavy Tank Armor does not have this flaw.
Around these levels First Tier Bureaucrat Armor isn't a bad option either, adds some nice HP and nano for the mid levels, and the gloves is especially nice with the +16 Pistol. Around 110 your should be pretty close to casting your top RK Charm Total Mental Domination so it should be quite possible for you to solo your Tier 1 pieces in Elysium and Scheol Catacombs, good place to practice your Bureaucrat skills.
For shoulder items you have Virral Triumvirate Egg's, Alvin & Dodga Shoulder pads (Quest Details on Anarchy Arcanum) or Barrow Strength from ToTW (assuming you have some pistols like CDR's equipped).
Levels 110-175: Those armors should serve you nicely still, however at level 147 you can use DeCranum's Corona MK II Armor that drops from Smugglers inside Smugglers Den. The droprate of this armor isnt the best, but the 980 HP and 49 NCU makes it a very nice set, especially if you do a lot of soloing, and apart from that, Smugglers Den is the Bureaucrat's playground, no other profession can solo this place from level 130.
Reactive & Proactive is also a nice choice from level 150, and can easy be used untill level 190.
A little known item for head armor is Spirit of Saccelum with a nice 400 HP, I still use this at level 216. Also Nelly Johnsons Little Black Dress or Meister's Reinforced Suit is a must have for any serious Bureaucrat, even if the mods on them arent that nice, this is the pieces of armor that sets us apart from all the other professions.
Levels 175-190: Azure Reveries with Heavy Notum Tank Armor is a solid option, has lots of nice mods for Bureaucrat's, best pieces is Chest, Boots and Gloves these should be the ones to go for first. Getting to Merc raids at this levels can be very hard, chances are you wont get these on this side of TL7, but its a nice set of armor worth some work to get. If you cant get it, previous armors will do OK, afterall we do not get hit that much.
Levels 190-205: For clan Superior Sentinel isnt half bad, for Omni Omni-Armed Forces. The Omni Armed Forces Tank Armor is a good alternative instead of a Notum Tank Armor if you are Omni. Exterminator Unit Chest Plate will do as well
Levels 205+: Armor of Merlin is a good option for TL7, has a nice add to HP, nano cost on sleeves and 25 Stamina on chest (and the +AAD fits nicely with your HM/CP/CiB setup), which will be handy for your 2 sec heal tick very soon. The helmet isn't particular interesting, though the +25 sense can come in handy for equipping Symbiants, just like the +15 Agility for each sleeve. The set has no pants, Superior Sentinel or Omni Armed Forces will do good since they add more HP, or you can use a piece of AI armor, something that adds to nano skills would be ideal for level 205. Kegern's Molybdenum Plate and Jathos' Molybdenum Plate is very solid options as well, though getting it from the Biodome can be a lengthy process
Its a good idea to look at the individual pieces, some might be better for you depending on how you play or where you play, and how your funding is. As Bureaucrat the Spintooth bosses that drops the Merlin Armor is soloble with a bit of practice, so getting some pieces is doable even if you don't have 150mill for a full set.
Tier Armor have had very little mention, this is due to the fact that it isn't that good compared to the effort/cost it takes to get it, with so many nice free armors avalible, there isn't much point in spending 50mill+ per piece of Tier 3 armor or the weeks/months it takes to farm it.
A closer look at Chosen/Faithfull Bureaucrat Armor:
Boots: Nice HP mod and AC but for Pistol/MBC/KSMG users the OTAF/Sentinel boots are better imho.
Cloak: Nice AC but i would prefer OTAF Tank Armor or HNTA or Merlin Coat or Spirit Shroud or ... over it
Gloves: Worth having. not uber AC but the mods are very nice, especially the adds to Pistol, by far the best piece. Also a decent HP modifier on these gloves.
Helmet: Aka the Fork Helmet. it is a good item with good AC/mods on it. It's worth the trouble getting it. Altough the Sentinel/OTAF has some other mods worth considering depending on your playstyle
Pants: Low on AC but the other mods are all very good. Worth the trouble. Especially the CL mod which you need if you raid pandemonium.
Shoulder pads : 300HP per side with 6strenght and 275 AC. Yep sounds like a good deal to me.
Sleeves: Seem not so good. Merlin sleeves will add to nanocost reduction and have higher AC. Only the HP mod on them seems good.
Body: Decent AC but only half the mods are good for us and it lacks a HP mod...
As a full set maxed out to QL300 it isn't all that bad, it has a lot of HP which is good for Bureaucrat's and adds a bit of PM/SI skills as well, however once you can max it out around 215-217, there is also a lot of nice AI armors and some of them aren't really that expensive compared to the Tier 3 set, and you will also have access to the armors from Pandemonium at this point, so you might want to consider what pieces will benefit you most.
Ofab Bureaucrat Armor is a valid choice as well, looking at the QL100 set it has many more advantages over the Tier 1 set, and opposed to other cheap Armor option, it also adds some Nano skills, Nano pool, Nano cost and Nano Init. that is very useful around these levels, in all its a pretty solid set compared to other options avalible. A set of QL200 Penultimate Ofab Bureaucrat Armor looks damn nice spec wise, lots of useful bufs for a Bureaucrat and far more useful than other armor options until TL7, after TL7 the set becomes less interesting, but there are still some nice pieces that can be used even at end game, Gloves and Helmet is pretty good compared to other options and even a full set would be OK if you are planning on soloing a lot in Inferno.
Alien armor's:
Combined Officers/Scout: Are a solid option since we are a profession mainly defendant on nano programs, Calms need alot of attack skills to be realy effective, so if you are very much into calming, these are it.
Combined Paramedic for the soloing Bureaucrat sounds like a plan, has loads of HP, so if you are going for a HP setup or is nanomage, Paramedic is a solid option.
Combined Sharpshooter's for the Bureaucrat that wants some personal damage and wants to consider the PvP option
The is really a mix of the different armor sets along with some Pandemomuin stuff in it for the 210+ crats out there, again it really depends on what you are doing with your Bureaucrat.
According to your own playstyle try to max out your HP if you solo. Go with weapon skill mods if you consider PvP or are a dedicated team player or just leveling, and fill up in nanoskills where needed. etc..