I =need= my
shovel (regular ol' digging shovel, not some sissy square spade or anything like that (well ok I have one of those too

) and my
scalloped bread knife (for stripping turf to enlarge beds under shallow-rooted trees, pruning, deadheading, making holes for transplants, dividing, root pruning, you name it), and
large containers (such as muck buckets, galvanized washtub, wheelbarrow) to transport bulk stuff to the garden and to the compost pile and chickens.
It would be inconvenient to have to go without a trowel, work gloves, metal bow rake, digging fork, pruners (hand and pole) and stakes; but I would survive.
I own a few other things, mostly @$1 from garage sales and auctions, which are useful occasionally but mostly sit in the garage: a hand hoe, pulaski, digging bar, the aforementioned square garden spade, pruning saw, etc.
Note that I do not own a regular hoe. I prefer to mulch and hand-weed. Never been much good with a hoe, I seem to lop off the 'good' plants and not be able to get at the weeds very effectively. (Of course, my real problematic weeds are *perennials* anyhow, for which a hoe doesn't do a huge amount of good). A few scrapes with the hand hoe (for perennial beds) or back of the metal rake (for veg garden) early in the season, plus mulch and hand-pulling, takes care of it pretty well for me.
My suspicion is that most of the funky hoe styles are better tried out in a friend's or neighbor's garden than bought on spec for your own

Then if you find one you really fall in love with you can get that one.
Pat