Tips for required tool equipment

Since you are moving into a new building, maybe this is somewhat less important for you, but a decent industrial vacuum cleaner (Starmix iPulse) has served me best so far. However, I had tiles removed in my place, which generated a lot of dust. But also for sawing, drilling, and sanding work, extraction is useful if you don’t want to clean the whole house for days afterward. (With gypsum and cement dust, cleaning is still necessary despite extraction.) I have also used the device for the car and the leaves in the gutter. Fortunately, I didn’t skimp on the device and have not regretted it.

Since you are talking about precast concrete parts, a rotary hammer is definitely the first purchase I would make. What’s important here are decent drill bits that can handle steel reinforcements and don’t become blunt at the first hit.
I didn’t buy a complete toolbox, rather a decent basic equipment that can be expanded with every task. Some “heirlooms” from relatives were already available, which still serve well. If you have nothing at all, such a box may make sense, but then you should pay some attention to quality.

Dowels: I bought a set from Fischer, so you have various sizes at hand initially.
Nails: I wouldn’t stockpile large quantities. Maybe some decent steel nails; others you will never get into your concrete walls anyway. I have already had problems with nail clips for electrical wiring on lime sand brick walls in the basement, so I preferred to plug plastic pipes with the matching holders, in which the cables could disappear much nicer.
Screws: You never have the right ones, no matter how many you acquire in advance. I have a set of chipboard screws and some packages with common sizes from the Praktiker/Bahr insolvency clearance sales back then; otherwise I only buy as needed.

Push lawn mower: I can’t say anything about it. With my 300 sqm, no option. I’m currently thinking about a battery mower; the cable of the electric mower is often in the way despite practice, and you never have both hands free, because you always have to hold the handle of the mower; otherwise, it shuts off for safety reasons. Therefore, better a battery mower.

Garden tools: I took them over with the house. A long-handled pruner for cutting branches at height, a battery hedge trimmer, and a battery grass shear for the lawn edges have been newly added. Brooms, snow shovels, etc. were available or I partly already had them.

Cordless screwdriver with impact function. Maki... offers very good cases for around 200 euros.
Tool cases with everything are available from 50 euros. For 100 euros, almost everything is included to be able to do something at home.
Dowel set from 5 - 10mm are the most common.
Spirit level 1m.
Screw set from 35mm to 60mm.
That was the first thing I got, and the rest comes gradually.

I don't have nails because all pictures, etc. were hung with anchors and screws.

Only buy tools and machine tools of at least semi-professional quality, no hardware store products that only last 2 years with intensive use. I wore out various "inexpensive" machines during the construction of my own house before I treated myself to professional quality. You should spare yourself this mistake—in the truest sense of the word—because buying cheap and building cheap ultimately becomes expensive. In any case, I strongly advise against so-called "sets," especially screw sets. You will never need most of it; the quality is mediocre. And as a strict rule applies: no slotted or Phillips screws. Only Torx/hex socket screws. Buy only what you really need and get advice from craftsmen.

The rotary hammer is the specialist for concrete; useful when drilling a lot and regularly in concrete and necessary when larger diameters are to be drilled (socket installation ...). The hammer drill is the all-rounder, can (without hammer function) also stir paint or drill wood and is sufficient to occasionally drill concrete (smaller/normal diameters, suitable drill bits assumed). The latter, in good quality, is for me one of the very few "must-have tools" (see below).

A cordless screwdriver is IMHO(!!!!) only useful/necessary for specific large projects. A normal household, where there is occasional screwing to do, gets by well with a screwdriver set. Always ready to use and needs no power, never breaks, the grandchild can still use it (people have supposedly even seen worn-out, broken screwdrivers, nevertheless ...). But that is probably a matter of personal attitude (cf. also the question about the lawn mower).

Have these already been mentioned?
- Water pump pliers
- Silicone sealing tape
- Pliers
- End cutting pliers
- Hammer
- Allen key set (needed for all kinds of adjustment screws on furniture and/or doors)
- Knife (cutter knife, good pocket knife, carpet knife)
- Flashlight (possibly as a headlamp)
- Small set of small screwdrivers (battery change on the son's Brio train)
- Tesa power strips
- Glue
- Battery charger

In a *complete* toolbox, much is naturally already included ... Open-end wrenches (sizes 8 to 32, two each), socket wrenches (likewise), bit set (slotted, cross slot, Torx, who knows what else).

Then there are the machines:
- Jigsaw
- Circular hand saw
- Table saw
- Band saw
- Belt sander
- Dremel
- Grinding machine (sharpening drill bits)
- Compressor
- Hammer drill, rotary hammer
- ....
==> Here, in my opinion, one should proceed selectively, possibly also consider borrowing. Most things are needed eventually for a project, but is it always worth buying? If you buy cheap, it only lasts once; if you buy expensive, you have dead capital afterward. Tough decision.

In addition, there is various special equipment for hobbies, bicycles, and cars ... depending on taste.

A cordless screwdriver is a must, I think. Otherwise, pretty much everything essential has already been mentioned. I also have a heavy, old, and almost 40kg vise... anyone who learned to file "on" such a thing won't want to do without it later. And also a Flott grinding machine. I am still missing a floor or bench drill, but that certainly doesn't belong to the basic equipment. A proper ratchet set, on the other hand, does.