[Radek]

1. Don't do it! The unarmored skill won't give you enough protection later in the game. Moreover, training an armor skill gives you "points" for AGI and END (it depends on the armor) when you level up.
Train Light Armor if you want to be a monk. There is a splendid light armor (the Glass Armor) in the game. There is no good medium armor in the game (unless you install some mods and except one cuirass) so that bad value for medium armor is no problem. There is an even better heavy armor (the Daedric Armor) in the game. Well, you will need STR over 100 if you want to wear Daedric Armor, moreover, a monk in a plate mail is a bit strange.

2. You can join the Fighters Guild, the Imperial Cult, the Temple, well, why not, the Mages Guild. Monks are always a bit mages. You can also join the Telvanni House (the house of mages) or the Redoran House (the house of fighters). The rest of the guilds are assassins, thieves, or knights, which you don't want to be most likely.

3. Don't do it! in a plain game. There are some mods around, which enhance the hand to hand combat but the hand to hand combat in the plain game is completely unsufficient for fighting. Install the mod or you will need a weapon.
You can use staves or maces, if you want to be a "monk-priest", you can also use exotic weapons, for example katanas. Why cannot a monk from far east use katanas?