Deutsche Rentenversicherung should send you an estimate of how much pension money you are going to receive every year. Assume that is optimistic, but a good baseline. I assume the matching program you mentioned is a Betriebliche Altersvorsorge (bAV)? Those usually also tell you how much they will pay you as a minimum, and another estimate based on normal economic growth.

Chances are that those together will not be enough to match your wage at retirement. So you should plan your savings so you can cover the difference for at least 16 years (which is the current life expectancy at 67 years old in Germany), and overshoot that if you can.

You have to prepare for the public retirement system (and also the small state pension system) to be insufficient. The system is currently designed to fall short intentionally! Most sources recommend to save 15-20% of your net income for your retirement. If you really want to be safe, I highly recommend that you calculate your actual pension gap (that is the total sum of money that you will need to spend the rest of your life after retirement to keep your current quality of life). Once you know the total amount of money you need, you can then calculate what your current pensions sum up to. The difference it the gap that you need to save. When you know how much you need to safe totally, you can calculate what savings rate you actually need at minimum to keep your lifestyle.

https://en.wikipedia.org/wiki/Pensions_in_Germany

I think you want to have all three pillars going, normally you save in some kind of stock market pension fund.

I don't live in Germany, but lot of countries in EU have similar system. Over here in Sweden, you can easily see an overview and your projected pension at retirement age by logging into one of government offered e-services, maybe Germany has something similar.

What number you need to reach - is completely up to you of course.

Over a full career, saving 10% of your salary can allow you to live comfortably in retirement with minimal government pensions. Depends on your overall salary of course, but 10% is a good start. 250 euro a month tucked away in an account that only earns a very mediocre 5% per annum would still have you almost 400k after a 40 year career. Obviously investing more and getting a better return could lead to much much more than that. A 400k annuity at retirement age would basically continue to pay 3k a month for well, as long as you need it.

I don't know German retirement systems, and I'm not a financial professional. But if you have employer match contributions, talk to them to see if you can max it out.

Outside that look at savings in tax-free envelopes here we have ISA's Americans have ROFFS? I think.

We can have a stocks and shares ISA, my personal strategy is to use that with a low cost all world ETF and a little bit in safety nets like gold and bonds.

Look to investing in a Sipp if you want to contribute more and handle a retirement fund yourself, again not sure how applicable this is to Germany.

If you just want to save, look at something similar to a cash ISA AKA something that is Tax-free and has an interest rate that will outpace inflation.

Clearly you must invest a considerable sum (at least 1/10 of your salary) each month , government pensions will continue to decline in value. It’s probably best to spread out your savings with a diversified approach (stocks, pension fund, realty).

Also consider the form of these savings. Keeping everything in financial assets might be very dangerous on the very long term. The chances of a world war and/or a financial collapse of the West are relatively high and you don't want a hyperinflation crisis to destroy all your savings. It happened in Germany, it is happening again in some parts of the world, it will happen again.

You don't have to save anything. If pensions are not enough to live (which they won't be if you don't save anything yourself) you can get social security for the rest. Obviously you will be poor.

The public retirement system will send you a letter each year telling you how much it will pay out if you keep paying like you are currently. Then just see if that is enough for you and if not, do something privately.

When you have more than enough money, and want to do something privately, just do yourself a favor and go pay an investment advisor (not working off commission). Never just "save something" in your bank account or whatever, always invest in the stock market into index funds. IMO, if you currently can't afford an investment advisor, then you also shouldn't save for retirement. Just enjoy the money you have now and live off social security when you're old.