Thread has a generic name so it can be used by other posters. If there's already a thread for this, I apologize; I didn't see it on the front page.

What's a good set of mods for if you just want to play an ordinary character, do some weapon-smithing, beat up the odd bandits, and not worry about dragons, blades, or the civil war as more than background, please?

This request is so vague to be meaningless.

oh boy...lol

I am going to respectfully disagree with the people who posted before me who said the question was too vague and meaningless. I did see a specific question in the OP and I have a specific answer.

To play as an "ordinary character" I am going to recommend three mods: Requiem, Alternative Start and The Notice Board.

http://www.nexusmods.com/skyrim/mods/19281/?delevels the world to make you start out as an ordinary citizen, rather than an overpowered person who can take on nearly everything in the game at first level. You start out weak and very ordinary. But the world is deleveled, so as you increase your character's perks, skills and attributes, the world will not scale with you as it does in the vanilla game. The world remains the same throughout the game, so you don't feel like the world is revolving around your character. Rather you are an ordinary person who may or may not advance to a position of great power, depending on how you play and where you put your perks.

http://www.nexusmods.com/skyrim/mods/9557/? lets you start somewhere else other than Helgan (you have many options where to start) so you can avoid the "Dragonborn" trope entirely and just start playing as an ordinary person.

Finally http://www.nexusmods.com/skyrim/mods/70142/?, will provide things to do other than Skyrims vanilla questlines, which for the most part all suffer from "chosen one" syndrome. The Notice Board adds an endless supply of radiant quests you can pick and choose from.

Personally, I would not want to play without these three mods in my load order, in large part because they make characters start out "ordinary" and give them the option to remain ordinary or become extraordinary.

EDIT, because the OP mentioned weapon smithing, I will add recommendations for Complete Crafting Overhaul, Weapon and Armor Fixes and Clothing and Clutter Fixes by Kryptopyr with the Requiem patches for each made by Unmeix. That combination makes smithing more interesting.

Thank you; those mods sound like they pretty much exactly answer my post.

IF you want dragons, but not to be Dragonborn... "You are Not Dragonborn", allows for vanilla dragons... add in any of the mods that make dragons harder if you want.

I only say that because I happen to like dragons. .but then again, I'm a glutton for punishment and also have "Immersive Creatures " & "Deadly Dragons ". My ordinary characters cringe when they hear a dragon and run....fast. I change the settings so that those guys don't get dragons alot.

The best answer depends on what the OP means by normal. The question isn't meaningless, but if we knew what was being sought it would be easier to give better answers. In general the skill systems make it fairly easy to make a normal person and do a lot of the things that normal people do. I'd advise mainly not abusing alchemy loops.

Become a Bard.