You can indeed use the military screen, and assign whatever you want your dwarves to wear, to them.
Exception being, dwarves with mining / woodcutting / hunting(?) enabled. These jobs have an 'uniform' of their own (being: wear nothing at all except the tools you need for the job)
So what I do: all my civilians go into squads (I prefer squads of 5 dwarves, but that's up to personal taste), and are assigned armor (and/or clothes, and a weapon).
Note: change the 'over clothing' option to 'replace clothing' to have full control over what the dwarf wears.
All miners and woodcutters also go in a (single) squad, but are not assigned any uniform.
There are some reasons to do this. The first, obviously, being armor protection. Getting most of my dwarves into full steel armor plus some cloaks is my first priority on most forts now. Not only will this protect your dwarves from enemy attacks, but also from dwarven Justice.
The second is less obvious; dwarves without shoes will pick up contaminants when walking over them. The resulting long lists of guck clotted to your dwarves will put an extra strain on FPS. Or worse, shoeless dwarves are much more at risk of FB poison exposure.
All the info you'll need on what / how much / in what order dwarves can and will put on clothing/armor you can find here, at the wiki:
http://df.magmawiki.com/index.php/ArmorEdit: important note: in the military screen >> supplies, tell your squads to *not* take any food. It is currently bugged. Having them take 'any drink' is fine though. They will need waterskins or flasks for that.
In answer to your other questions: dwarves cannot wear jewelry and such in fortress mode. They can in adventure mode.
In previous versions, I've had dwarves stock up on lots and lots of worthless items in their personal chests. I think that was after the economy set in though.
In this version, I've not seen a dwarf own anything except clothing yet, but I haven't gotten to the economy in the current version.