Here are my 2 ct, mainly in addition to what Philipp and NegativeFriction write.
At some point you mention €, so I assume you are in Europe. Compared to the US/North America, this means
- your chances to learn/study a professin without going deeply into student debt are great. You'll probably not need to reserve most/all of your money for tuition fees.
- As for the various suggestions to invest into real estate, at least here in Germany I'd definitively not recommend this at this stage: better postpone that until you have a realistic estimate that you'll stay at one place for the longer future.
The situation in your country may be different, though.
You seem to have a good grasp at your finances and also a rough plan of what fractions you may want to put into which "bin" (bookkeepers would call it account). That's a great start.
I'd recommend to classify these bins into
- long term investment money (saving as in retirement)
- medium term investment money (as in saving to buy a house in 10 years)
- play money: a part of your money that you put into high-risk (financial) activities, and that may be completely lost as a result.
- consumption: savings in order to buy stuff that is either directly consumed (as in vacation or ice cream) or that will probably depreciate in a way that you cannot rely on getting anything substantial for selling.
This includes possibly a car (in mid future?, but also your lab)
I'd recommend to set upper limits for yourself for the play money and consumption categories (separately) and a lower limit for the long term savings/investment. Bot in terms of absolute amounts and of fractions.
IMHO it is a good time to start investing: starting now will allow you to learn slowly along the way.
buying some shares [...] deep knowledge [...] a little bit more than 20% of my money.
Others have told you that investing in single shares is a risky decision, and that deep knowledge often turns out not to have been all that deep. That is of course true, but it is maybe nevertheless worth while in the sense that putting a limited amount of money into some shares you'd like to buy will get you experience with the procedure, and after a year also with the taxes and so on.
Many brokers charge a minimum order fee, so it makes sense not to put too small an order, but 2.5k€ or 5k€ would probably be a good size.
Due to the risk of a single share investment and the risk inherent to doing something risky in which you do not have experience, this falls into the play money category.
(At some point in the future, you may want to excercise the same strategy to check out, say, bonds.)
However, this is also a great point to start a habit of long term savings. Others have explained that at your stage of life/wealth ETFs are the financial instrument of choice. So the recommendation would be to start your long term savings this way. You may want to put a lump sum now, but check out with your broker whether they offer savings plans for ETF and what the conditions (fees) are for that. With 900 € per month of which most is disposable income, I think you can put maybe 400 - 500 €/month into such savings plans.
Yes that's quite aggressively saving, but you'll probably lower that somewhat when you move out of your parents house. Until then, an aggressive savings plan can at the same time give you a head start in terms of saving and keep you out of lifestyle creep (in the sense that due to your exceptionally low expenses you may be tempted to get a lifestyle that you could not really afford if you'd have to pay for all your expenses).
Starting a business
5k investment into a small business I would like to start which I hope to be profitable in one and a half years.
That's play money as well: the risk of loosing that money is very real. Many small businesses are shut down again within few years and the fraction of successful businesses increases with the age (or rather professional experience) of the founder.
Personally, I kept the idea of starting my business "in the back of my mind" since before I graduated (I'm chemist). In consequence I attended some business administration lectures for non-economists (in the evening: they did draw the correct conclustions from analysing their customers) and business starting workshops while doing my PhD. I also started slowly by signing up with the tax office as freelancer which in my case allowed a small/low risk strategy: I was able to do this as a side line that was profitable when a customer came along, but had hardly any fixed costs (full personal liability, though).
After some 15 years of professional experience, I decided to seriously get into business (with a GmbH, i.e. limited liability).
In any case, I recommend that you learn about how to start a business: there's lots of information around, but sometimes it's hard to find it when you're not yet into that crowd.
Where I am, there are
- events such as a business starting day in November
- a local technology/incubator center runs a series of free workshop ≈1 evening each month on topics like bookkeeping/acounting basics for small businesses, legal topics, financing topics,...)
- there's a business founders' regular table
- the chamber of commerce offers free initial counseling on starting a business (and they know all the others who have information)
- the local university has similar counseling and also lectures on business administration for founders (no need to study business administration, if you have another profession. But if you want to found a business, you really should have basic knowledge of B.A.)
Others here told you that if you go for it, you should make sure of limited liability. I'd recommend to get counseling on that: I don't think that such a recommendation can be given that generally.
Laboratory and self study
small laboratory of technology for myself [...] learn new skills [...] business I am eyeing for in a more distant future [...] 2-3k.
Have a look around whether there's a suitable maker space or hacker space or the like where you could go.
Not only would that give you access to "machinery" that would cost you a lot more than 2-3 k€, you'll also meet and network with people who learn new technologies and share their knowledge. There's also a certain overlap with the business starting scene.
Oh, and while maker spaces and hacker spaces are mostly focused on computers/robotics/mechatronics, I've met people setting up physics and biology experiments.
As you mention in your comment that you want to look into AI and someone commented on the need for heavy computation machinery: I (my company) do machine learning for chemical data. Most of the modeling I could do on my laptop which I bought 1 1/2 years ago for ≈850 € (used Thinkpad). I do prefer my desktop though for day to day work (which also has a bit more compuational power). All in all, the machinery for my business would fit into a 2 k€ budget (if needed, servers can be rented in addition, of course - if the customer agrees to their data leaving our house).
However, other application fields for AI have data that behaves differently, and they do a lot more number crunching. I just want to point out that there are application fields where less fancy computers work perfectly well.
The more important part IMHO for you would be to get a thorough understanding of data analysis (see below), and that needs less computational power and more brain power and elbow grease (well, maybe rather brain grease...).
(I'm using the advantage that I know chemical data [after all, that's my profession] and that I can recommend measurement modes where physics/chemistry/biology gives us often rather direct ties between the data and the properties we want to predict.)
Learning/studying a profession
- You mention that you started a physics education but find it hard.
- You also comment that college-level physics education sounds good to you.
- And you mention your interest in AI.
Are you aware that you can study data science? Where I am that is possible either at university level (often technical universities) or at universities of applied science (more applied level). Not every university offers it, but the relevant courses may be hidden as specializations within studies like business-oriented computer science or the like.
I'm a chemist who moved professionally into the interdisciplinary space between chemistry, physics, computer science and statistics. That move happened during my Diplom [Master] thesis. When I was 18, I had a hard time to decide whether the profession to study should be chemistry, physics or computer science (I had no idea about statistics, as that was basically omitted in my school maths). And see what happened...
IMHO physics would also be a perfecty good starting point for a data science career. So would statistics or computer sience or mathematics.