I think it is worth organising it. It's easier to put away at night if everything has it's place. It also models good habits and I find my dd doesn't play with her stuff as much when it is all in a muddle - and then she goes and makes a mess with a load of other stuff elsewhere!
It's also easier to cull (we do this twice yearly - once before Christmas and once before birthday) if it is easy to see and access. Easier to share with friends too (when your dd is older).
I find it is good to decide on sufficient storage (with a little room for 'growth') then cull the amount of toys to fit the storage you have (and not the other way around if that makes sense)
I use two painted wooden tall bookcases (firmly secured to wall) with separate pull-out containers of various shapes and sizes on some of the shelves.
We then have two round paniers on the floor for her baby dolls and their clothes and accessories + another panier for soft toys.
One dressing up chest. One mini coat stand for bags (if your dd is like mine, she will have acquired 30 hand-bags and purses of various shapes and sizes by the time she is 7!! I don't know where they all come from even though we cull ruthlessly - down to 12 currently!)
Bookcases are good because you can keep the more delicate/precious/annoying toys that go all over floor (eg Hama beads and marbles) right up at the top and the toys you are happy for your dc to pull out on their own, nearer the bottom. And books can be stored too of course.
They are also adaptable as they grow. For example, one of the bookcases is going to be repainted and put in dd's room soon as she is starting to play in there more with her friends.
I think I would go for Trofast if I had lots of boys - for construction kits and lego and stuff - but shelving works best for us (one dd only)
As for the hanging bag idea - I tried it and found it a bit fiddly to be honest. The bags (and their contents) usually ended up on the floor. I just reserve a row of pegs now for games kits, swim kit, school bag and coat etc etc and that works well.
Good luck!