The "most reliable" way would be to use a hardware TNC (
https://en.wikipedia.org/wiki/Terminal_node_controller) or Terminal Node Controller. While new, they can be expensive, on the used market they can be quite inexpensive (I got a pack of 5 for $40 US at a local ham fest). You hook the computer to the TNC, generally using a standard RS-232 serial port) and then the radio's microphone, PTT, and speaker connections to the TNC using the radio interface. You configure the TNC for packet mode, tune the radio for the desired channel and you're ready to go. You may also require adjustments to the audio levels, but this should be expected. There are newer ones that use a USB connection instead of a serial port, but those often cost more than the serial port versions.
There is also a way to use your sound card as a TNC. Often this requires a serial port to handle the PTT function as well. A Windows version of this is explained here -->
Introduction to Sound Card Packet with AGWPE <-- which should be required reading for anyone that wants a sound card TNC. There are both free (with only basic features) and for-pay versions (with extended features). The free versions has on-line support using various web sites and groups but due to the age of the software, these may not be all that current. Chances are the issue(s) you need help with have already been discussed by others so this probably won't be that much of a problem.
I won't discuss the legalities, mostly because I don't know the laws in Austria. Using FM, which I believe is allowed in your country, you can generally use 1200 baud while on AM/SSB you will probably be limited to 300 baud connections. This is mostly due to the clean audio you get on FM while on AM/SSB there's lots of noise and static that will interfere with the signals.
