I take it that prewar books are no longer collected for a quest, as there are a lot in the docs shack. If this is the case then I don't need to bother collecting them?

Should I bother collecting Sugar Bombs, infact what should I look out for?

Now that I've just downloaded the classic pack that came with the game do I need to be connected to Xbox live whilst playing?

Most of the collecting quests that are vital / very helpful to resolve story quests are given multipule choices to resolve.
Some are skilled based others can require different objects based on how you wish to pay ( or if you wish to pay at all ).
In all / most case the collection of objects for story quests is pretty easy and requires just strolling to a few areas at most.

Pre war books no I've yet to find even an unmarked quest for these.

Scrap metal, missiles, any metal such as tin cans, stip packs, rad away, fixer, dog tags, Legion ears are the most common off the top of my head.

You will however check both the workbench and campsite to see what recipies require which objects as the lists can get quite complicated.

Also as a hint keep some scrap metal / electronics, conductors, fission batteries and sensor modules handy early on in a unowned sunset sasprillia crate as you may find you need them early on at some point.

Thanks.

Would that crate be in the docs shack?

Doesn't matter which crate, as long as it's not owned. If you don't have player housing yet, I'd (for example) use
the lockers inside the Good Springs school to stash some stuff you think you might need in a later point in the
game. Once you finish the quest in Good Springs, you can also use some containers inside its Gas Station,
it also has a bed you'll be able to use. Good luck

Thanks for the advice but just one thing, I take it that if the name of the object is red then it's owned by someone. I'm only asking as the crate I mentioned is in the Docs shack but the name isn't in red but is it still his property as it's in his home?

You can use the crate in Doc Mitchell's house, but it's not wise to store your things inside a 'cell' (in this case Mitchell's house)
where an NPC wanders around. I'm sure he'll leave scrap metal alone, but if you'd stash food or drinks or weapons in a cell where
there are NPC's it might not be safe, as in they might take it.

Thanks.