If it were my house, I would install the Closetmaid ShelfTrack system. I would put the shelving across the back wall and at least one side wall. The closet seems too deep to be able to reach in.

What kind of door is on the closet? Can you change the door as part of the renovation? How big is the opening to the closet?

It's hard to give suggestions without knowing more about the closet or seeing a picture. For instance, do you have bi-fold doors that open completely, allowing easy access to all parts of the closet, or is there a single, normal door, making it difficult to get to the sides of the closet?

The closet opening is full width and height and there is not a door on it currently. Adding a door will be part of the project.

Why is it raised 4 inches off the floor? Can that 4 inches be leveled? Might make the inside more accessible and therefore more efficiently used?

I would suggest you find a style of bin you like that could go on a shelf. Most would require probably a 15 inch deep shelf. Then plan to fill up the shelves (mostly) with the style bins that you like and label. Except leave vertical and horizontal wall space for vacuum...

One of the hardest parts will be to figure out how to store vacuum so you might consider that first before the bins - what part of it can be hung? Can attachments be put in a bin? Need to store bags in a bin? etc. This will take up a fair amount of room (at least it does in my closet) so that is reason I suggest starting here. Perhaps you can find one of those horizontal racks that allow you to clamp a broom/mop/vacuum cleaner hose in each individual clamp (maybe 4 or 5 clamps).

I don't think you have room for linens. what about using a rollout tray that fits under the bed? You can get one for each bed and put linens (probably room for extra towels depending on how many beds and maybe even table cloths/napkins?) I just saw this idea on the "neat" TV show that just started appearing on a local channel here on the subject of helping people organize. If you have a lot of linens, it might work well especially if there is a lid on the "tray" that slides under to keep out dust.

I'm in the process of dealing with these issues so will continue to pay attention here to see if I can find help - I'm thinking a "broom closet" needs to be dedicated pretty much to vacuum/broom/mop/bucket/dustPan/cleaningSupplies/a.c.Filters but maybe I'm wrong.

games can go in bins. Air conditioning filters go on top shelf?

I agree w/ not trying to wedge ALL of that in there; put bed linens by the beds they go on somehow. And I'd vote for board games somewhere else as well, if at all possible.

And seriously look into back-of-the-door solutions to make the most of the depth, and to create accessible compartments for often-used things or smaller items you want to be able to access easily (like vacuum cleaner bags).

Also consider shoe pockets or something on the side walls in front of the shelves.

If you're going to set the vacuum cleaner on the floor, then put stuff you don't use very often in the boxes behind them.

I agree w/ having a few wide shelves for wide, flat things.
And don't have TOO great of gaps for shelves--esp. w/ board games, you don't want to stack stuff too many items deep, because then you'll be discouraged from using stuff on the bottom.

I keep thinking of the idea of having custom wooden shelves/dividers, etc., so you could have a little "cubbyhole" for the vacuum with other shelves around it.

See the tower shelves here?http://www.marthastewart.com/267639/kids-closets

Put something like that in there, and then use the sides to attach shelves to. If you took the shelves out, maybe the vacuum would fit in the gap, and you could have shelves next to a tall empty space.

Here's another example of using bookcases/shelf towers to attach closet hardware to; you don't need the rod, you said, but you could attach brackets for shelves.
http://www.marthastewart.com/266731/walk-by-closet

BUT ESPECIALLY look at this,
http://www.marthastewart.com/272404/tame-the-broom-closet
and the not-uniform cubbies created by the wooden dividers, esp. the vertical ones. (And if you're at all interested in this sort of thing, go look at the Kreg Pocket-Hole Jig videos on YouTube.)

You don't have to turn the WHOLE closet into something custom; but you could create ONE little custom-sized cubby for the odd-shaped thing (like the vacuum cleaner), and then rig up adjustable shelves on the rest.

And of course, Martha has left a lot of photogenic space in her design, etc. But you could easily put a lot more stuff in that space.

Re: the shelves: I always want to install those little strips w/ the slots, like they have in library bookshelves, in closets like these (since there is a left wall and a right wall, sort of like a bookcase) so the shelf supports don't really impinge on the storage space. (the rear-wall-mounted brackets are triangular-shaped, so you can't space the shelves as closely.

Once you decide what cleaning supplies you need, look into hooks, etc., to put on side walls or back of door.
http://www.marthastewart.com/268077/broom-closet-organizer

Pegboard would be great on the sides of the closet in front of the shelves.

MikeAndHike--I ran across some things on Pinterest that made me think of you.

Let me know if you can't get into the site; I don't know if you need an invite anymore.

A wall of pegboard for cleaning utensils. this is shown on a wall in the laundry room, but you could do it on the back of a door or a side wall in the closet
pegboard

This is a standalone dresser, but I'm showing it to you to show the difference in the spacing of shelves, etc. See how on one side the cubby is taller than the other side w/ its shelves? That's the sort of think I was thinking about for the vacuum cleaner (if it's a canister, a shorter opening; if an upright, a tall one)
asymmetrical sides of a storage area

Here's another example of custom cubbies of various heights and configurations. This is under the sink, but it's the general idea. Just scale up to fit your closet
custom cubbies of various heights & configs.

Another example of differently proportioned cubbies--again, in a smaller cabinet, but just scale up to leave a space for the vacuum cleaner, and then fill the rest w/ shelving.
differently proportioned cubbies

This has way too much open space in the middle, given that you want to store games, etc. But it shows a back-of-the-door set of pockets and hanging stuff on the wall.
back-of-the-door pockets

This is a rack mounted on the side of a bookcase, but it's actually designed to go on the back of a door. Nice big square baskets. And it's adjustable. You can get it at the Container Store. And you could conceivably put something like this on the wall in front of the shelves if you left a gap to set the vacuum cleaner in.
back-of-the-door rack

This uses even larger wire baskets to put stuff in (personally I'd space them a bit more closely so that I could get another basket on the door--you just need to leave enough headroom that you can actually get stuff out).
large wire baskets to wall or door mount

This one is dedicated to cleaning supplies, and you want to have more stuff in there than that, but it might give you ideas for storing stuff.
cleaning closet

And this classic--storing the bottles in the shoe pockets. If you don't have that much cleaning stuff, then other pockets could hold other stuff (flashlights, etc.). You can even put stuff like cleaning rags in there.
clear shoe pockets for cleaning bottles

Here's another back-of-the-door option--build a frame and put shelves in it. That could hold a lot of stuff, maybe even frequently used games.
back-of-the-door wooden bookcase

And here's an example of what I meant by mounting stuff on the side walls in the space in front of the shelves (if there is any)
spice racks mounted on side walls of pantry

Just think of what you'd want to put there--cleaning bottles? Card decks? Vacuum cleaner attachments? dust cloths?--and pick baskets or wooden boxes just big enough to hold them.

Or, if the shelves some all the way forward, you could still mount something like this on the side wall just below the shelf.