You have pretty much described GURPS, with the exception that it 3d6 based rather than D20 based.
There are no classes, levels or alignments. Characters have a point budget to spend at creation with which they purchase basic attributes, advantages, and skills. Additional points can be had at creation by taking disadvantages which can also provide good role playing hooks.
GURPS does not require magic at all, but you can have it easily - the ability to use magic is an advantage, your skill with any given working is a function of the points you spend on the spell. These have a normal price, but if the world is set to low mana / magic then they are much, much less effective and thus have to be more narrowly focused to be useful.
Armor works exactly as you ask - it protects you but also encumbers you, reducing your ability to dodge or perform any action reliant on dexterity or derived speed.
You can try it with GURPS Lite, available for free here:
http://www.sjgames.com/gurps/lite/
Your players can actually get by with less (if you help them with character creation) using GURPS Ultra-lite:
http://www.sjgames.com/gurps/books/ultra-lite/
They actually have a published setting, Banestorm, that has the setup you are looking for, but that is not free.