How do I make this space functional, and inviting?

Hi Monica! You have a great space there, lots of room. You could probably fit a backpack storage bench there. I've seen some great DIY ones. This post shows a few IKEA hacks to get it done. Perhaps it will give you some inspiration. https://www.housebeautiful.com/home-remodeling/diy-projects/g2894/entryway-ikea-hacks/?slide=1

Add some pretty wall art or a big mirror (https://www.hometalk.com/diy/decorate/mirror/diy-wall-mirror-24747866) and then use those storage caddies to hold the shoes so you don't have to see them and to reduce the clutter.

DIY Wall Mirror

How about something like this?

https://www.hayneedle.com/product/homestylescabincreekhalltree.cfm

https://www.walmart.com/ip/Carrabelle-Entryway-Shoe-Storage-Bench-Multiple-Finishes/35285450?wmlspartner=wmtlabs&adid=22222222222024151672&wmlspartner=wmtlabs&wl0=e&wl1=o&wl2=c&wl3=10355566939&wl4=pla-1103086687426&wl12=35285450_10000001880&wl14=foyer%20storage%20bench&veh=sem&msclkid=8b9cb353618319003876e8e81d2b1b03

https://www.overstock.com/Home-Garden/The-Gray-Barn-Waggoner-White-Shoe-Storage-Cubbie-Bench/20306388/product.html?refccid=ZWBATAKGGUUYVG2NOVVSYQU75U&searchidx=19

https://www.wayfair.com/furniture/pdp/beachcrest-home-mckinley-storage-bench-seho1471.html

FIRST" TOO' MUCH IN ONE CORNER, SHOES SHOULD BE PUT IN ORDER ,BY THE DOOR WITH LARGE SIDE TABLE, WITH HOOKS ,FOR BACK PACKS, AND BAGS, KEEP ALL TIDY AND OF FLOOR, 'T

HEN DECORATE WALL WITH A TREE HOOK STAND FOR JACKETS OR OTHER, A NICE ROUND SINGLE MIRROR, AND KEY RACK, PUT SIDE BY SIDE NICE,

HI, A BENCH WHERE THE SHOES ARE, A MIRROR OVER UNIT AND A PICTURE

My approach would be to include several things.

1) Create a space for kids and adults to put coats, hats, etc. Each person has their own hook for coats, drawer or basket for stuff, etc. http://www.traditionalhome.com/design0/get-organized-mudroom-must-haves?page=6

2) Create a space like this with a nice table, mirror, etc. https://www.hometalk.com/diy/build/furniture/farmhouse-entry-table-36375287

we used to do the same thing. Mom's answer was to us--"take them to your rooms." then she did a nice entry table and decorated around it

I did two rows of decorative hooks. One at kid height and one at adult height. That way backpacks could be hung low and jackets could be put higher. Additionally I had a rustic wall mounted wire basket to catch the mail. Pretty baskets in your book shelf could catch gloves, hats and scarves or shoes.

You need storage unit with drawers/baskets for storage that's hidden. They have a small storage unit with hooks for jackets/hats/backpacks, pull out baskets that hold shoes etc. This way the kids will be trained to hang up and put away their things. This is your entry way and first thing you see upon entering your house so it must be kept neat and tidy. First impression. You need a organized place to put everything.

A little bench with some baskets underneath for storage. A mirror and some decor would really brighten it up

Actually, I like Por's answer - take your personal things to your room. And decorate the entry invitingly for all who enter. It will always look cluttered unless you can enclose all backpacks, shoes etc.

How about some built in lockers for coats and shoes get wood crates then attach plywood to sides and top add hooks

A nice-looking boot tray (I've seen some in copper), but only for parking wet/snowy/muddy shoes. One to a family member, and take them away when they're dry.

a small ladder attached to wall for shoes to go and put plant's on top

ikea has a great shoe dresser, paint it a fun color, or leave as is. Put a mirror over it, and family photos,framed kids artwork,a padded bench with storage (Ross, Home Goods...) on both sides of dresser, and hooks! Here are some great hook ideas, some to fit in the “art gallery” or off to the side behind door.

Depending on your budget you have a lot of options but a coat shoe rack will give you the storage you need. You can buy a whole unit (think IKEA, Overstock) or you can get the same effect with different pieces. Buy a bottom cabinet (Homegoods, etc.) and then use coat hooks on the top. Whatever you do be sure to have an element or two of decor items, a mirror, a picture and some pretty accent pieces. Here’s just an idea for you. Of course, if you or someone else is handy, you could build your own,

It cant be too complicated or they wont use it. I would prefer some kind of closed cupboard where they could just open the door and toss in their backpacks. Anything open wont be kept neat. BTDT.

Something like this might work. Depends on how deep the shelves are.

https://www.houzz.com/product/123510684-connaught-solid-wood-entryway-storage-cabinet-dark-chestnut-brown-transitional-buffets-and-sideboards

For the shoes I would do a bench behind the door with a tray under the bench for wet shoes. Oh and my friend gathers up all her kids stuff that doesn't belong in her entryway and tosses it down the basement stairs. Their bedrooms are upstairs. BTW.