When I run the launcher I see the "Data Files" option and see that only FalloutNV.esm is checked.
I'm trying to figure out when checking these things does exactly.

When I started the new game I get a bunch of extra items. I guess those aren't mod related? I wonder because I got some sort of caravan shotgun and see one of the un-checked mods is the CaravanPack.

Are the quests that pop up when I leave the doc's office mod related?

I usually play games mostly vanilla at first then go back for the mods. For this one should I just go ahead and check all these things and treat it as one big game?

What you are seeing is the DLC that comes with the ultimate edition, not mods (as long as you haven't added any mods). You can enable/disable DLC (as well as mods) from the data files option.

The data files window in the launcher can be used to enable/disable plugins, but there are special rules for DLC. Each DLC comes with a .nam file that resides in the data directory. These files function as a safeguard that forces the DLC to load even if they have not been actively enabled. If you wish to disable a DLC, you need to delete the corresponding .nam file.

It is also advised to do this if you want to do any modding yourself with the GECK, as the force-loading applies there as well and can lead to accidental DLC dependencies if you forget to uncheck them.

The .nam files are otherwise completely useless, so don't worry about deleting them or backing them up.

It's also worth noting that the game launcher is not a substitute for a proper mod manager. The UI breaks completely with even a small number of plugins and it does not allow you to manage the load order. If/when you begin modding, I'd strongly advise you to not use it at all and get FOMM or another manager instead.