Investing in Germany

Your tax class hasn't anything to do with your investments.

It only serves as a vehicle for your employer to calculate the taxes to withhold.

In class 1, you are taxed as a single with a certain tax exempt amount.

In class 6, there is no such exempt amount, as you have the exempt amount only once.

Be aware that you are obliged to file your taxes for every year you work on class 1 and class 6.

Besides, you won't have to pay taxes on the proceeds of your investments until these exceed 810 € per year.

If I were to start another job then I would have to keep one of my income to class 6.

Yes, but this is temporary. YOu are the unexpected to file a tax return where ALL your taxes and income is combined. All what the 6 does is force a WITHHOLDING at maximum rate, you then get the money back.

I would like to know if my tax class changes once I start investing my money.

Investments are taxed not by income tax but by capital gains tax normally - which is 25% or 0%, depending on length of holding. The tax class is for income tax and has NOTHING to do with investment. it also has nothing to do with TAXES - it has everything to do with TAX WITHHOLDING, to get your overpaid money back, again, file a tax return.