I used to use Duel Sheath Redux, but that mod actually messed up my game so much I had to do a full reinstall, it may still have problems, but be careful with it.
Are you using the Nexus site[footnote]This baby: http://www.nexusmods.com/skyrim/?[/footnote] for mods, or sticking to Steam, because that will affect the mods available to you.
Also first thing you should look at is installing SKSE. http://skse.silverlock.org/
A lot of the more ambitious mods require SKSE to work as it allows more extensive changes to the core coding of the game.
Large Popular mods for immersion:
Real Shelter [http://www.nexusmods.com/skyrim/mods/52612/?] (shown in the vid you posted) - stops rain and snow travelling through rooves and other cover while outdoors.
Expanded Towns and Cities [http://www.nexusmods.com/skyrim/mods/13608/?] More NPCs, houses and ornamental stuff around some major settlements. Compatible with Real Shelter.
Immersive Patrols [http://www.nexusmods.com/skyrim/mods/12977/?] Adds some skirmishes along the roads and forts between soldiers and bandits.
Small mods for immersion:
Various guard outfits for Every cityTS Edition [http://www.nexusmods.com/skyrim/mods/6770/?]
Fantasy Soundtrack Project [http://www.nexusmods.com/skyrim/mods/46518/?] More awesome tunes for exploring. It will amaze you what a huge difference a new adventuring song can have on an old, well trod path.
Follower commentary overhaul [http://www.nexusmods.com/skyrim/mods/52019/?] Adds in unused lines that were left out of the final game.
Guard commentary overhaul [http://www.nexusmods.com/skyrim/mods/23390/?] Same as before, but specifically for the guards, to stop them mocking you in later game.
Realistic Boat Bobbing [http://www.nexusmods.com/skyrim/mods/52694/?] Makes boats bob in water instead of being static.
Dynamic Loot [http://www.nexusmods.com/skyrim/mods/42662/?] Lets you augment drop ratios, add improved or enchanted weapons and armour to drop lists (and therefore enemies)
There are several mods that do the same thing, but with different takes on it. Probably best to read the descriptions / try them all out and choose which ones you like best.
Hypothermia/Frostfall - Mods that add negative effects from getting too cold or wet, right up to death if you don't get warmed up fast enough. These are the two most popular, you can search for others as well.
Camping mods, some of which are Hypothermia/Frostfall compatible (to provide shelter) allow you to pitch tents, fires etc. to make a camp for staying out in the wilds.
Various food/drink/sleep mods that add negative effects to going too long without them. Best just search them on your own on Steam/Nexus
And of course, weapons and armour pack mods.
Heavy Armoury [http://www.nexusmods.com/skyrim/mods/21120/?]
Weapons of the Third Era [http://www.nexusmods.com/skyrim/mods/12892/?]
Immersive Armours [http://www.nexusmods.com/skyrim/mods/19733/?]
Immersive Weapons [http://www.nexusmods.com/skyrim/mods/27644/?]
That should keep you going for a while (just try and pace yourself when adding mods - add them one at a time, then load up the game and try and access the content to make sure it works)