For this task there is actually a traditional Japanese tool which was purpose built for this chore. It is called a hori-hori and was designed for cutting through soil, sod, roots, clods, and weeds. There are a number of good manufacturers but I would personally recommend this one from A.M. Leonard which costs around $30.00
https://www.amazon.com/M-Leonard-Deluxe-Knife-Stainless/dp/B00UTOLNY4
Congratulations, on your new organic adventure! As far as tools, start with the basics, and add to your collection as finances allow. (I have bought some of my favorite odd, specialized tools at estate sales at very reasonable prices.) Here is a list of the tools that I use all the time:
I personally prefer tools with unvarnished wood handles.
No one has mentioned any gardening tools I don't think.
Bad clippers are terrible. They do damage to plants and are uncomfortable. Most people would recommend felcos, but they are expensive and personally not my favorite. Corona clippers are fine and like $30-40. I use these exact ones that are available just about anywhere. Been great for me. https://shop.coronatoolsusa.com/bp-3180-classic-cut-bypass-pruner-1-in.html Loppers and pruning shears have more niche uses, but they're sometimes helpful too. But not having a good pair of pruners is a huge PITA almost immediately.
In this vein, gonna need a digging shovel and a trowel. Type and feel matter much more than brand imo. Instead of a standard trowel, I would get a hori hori knife. They're like trowels, but strictly better. This one by AM Leonard is pretty much the standard high quality one, but you can get em for much cheaper. It is a knife, so steel type matters, but you're digging in the dirt with it, so it isn't the end of the world if it gets dull. You should get one of those diamond rod sharpeners (not a honing rod) to sharpen the hori hori knife and your pruners. Something like this.
Oh, and garden hoses! And a good hose reel. Opinions are all over on them, but cheap hoses suck. And a watering wand. Again, cheap ones are super garbage. Highly recommend a good DRAMM setup. It is what literally every good garden center uses to do their watering. They still can break, but nowhere near as bad. You gotta get a valve , a wand, and a nozzle. It looks steep, but your plants will thank you. Deliver water right to the soil instead of into the foliage and hoping for the best. The modular setup means when one part breaks, you can replace just that part. Super clutch.
Oh, and a fertilizer spreader! Walk behind models at the big box store are fine, but you can do much better on Amazon. $40 for something cheap in the big box store, or a much higher quality one for $100 or so from amazon. Much better feel and consistent spread with a quality that feels like it will last much longer. I think the higher cost is worth it, but not a necessity.
And a wheelbarrow! Especially if you aren't super strong, hauling dirt or plants around the hard can get fatiguing. https://www.lowes.com/pd/Kobalt-7-cu-ft-Steel-Wheelbarrow-with-Flat-Free-Tire/1000777746 is the exact one I use. It's pretty good. Opinions are split on 1 vs 2 wheels, and decent never flat vs bicycle pump inflatable wheels. I will say for very heavy loads, like when I load it up with rocks, the wheels do have trouble. Otherwise, I think it's obnoxious when your wheels need to be pumped up and vastly prefer this style. The 1 wheel is for sure more maneuverable, but so much easier to accidentally tip over.
Most routine gardening can be done with just that. Things will come up that you need specific things for. Like, when leaves start falling, you'll obviously need a rake (I have to deal with a lot of leaves and I like this specific one), but if you have a good mulching lawnmower, current best practices suggest just mulching leaves into your grass as they fall. Once a week or so. Or you might need a tamper, trenching shovel, and a hard steel garden rake if you try to do much landscaping like spreading mulch or whatnot. But that stuff can all just be picked up as needed.
Oh, and lots of pots! Can never have too many spare pots. Just like terra cotta pots for plants you want to bring indoors over the winter. Depends on your climate and your plant preferences though.
DeWit makes excellent tools that will last a lifetime. You can buy the complete line of Dewit garden tools on Amazon. I enjoy using garden tools made by Joseph Bentley, which are similar to the DeWit tools. (It seems like the Joseph Bentley traditional garden tools may have largely gone out of production.) Unvarnished wood handles feel nicer to me than plastic, rubber, or composite handles.
The tool that I use the most is a Leonard soil knife (a.k.a. hori-hori). The orange handle is eye-wrenching, but makes it easy to find when you leave it in a garden bed. The second most-used garden tool is a serrated trowel, like this one by Dewit.