Hi there scebab!
It is great to see that you show interest in music composition! In terms of Free DAWs, it is difficult to recommend especially not having knowledge on all of them but also some are stronger in some aspects rather than others. Like Pro Tools First has limitations, but as a starter DAW for music production it is great to learn. It is a steep learning curve, but it will definitely help you in the long run for audio production in general. Most DAWs generally have the same concept of how they work and what they do. There are some that are completely different and throw you off. But learning Pro Tools First, with it being a more advanced DAW, will give you the knowledge and the tools to navigate and use other more intuitive DAWs like Logic Pro and Cubase.
Free DAWs that you can have a look at is FL Studio, Studio One, Ableton Live Lite, GarageBand, Cubase LE, Ohm Studio.
Depending on what OS you are one (Mac or Windows) will depend what you can and cannot use.
For Mac, GarageBand is literally Logic's little sibling. It is very useful, intuitive and powerful for a free product.
A not free but very CHEAP option is REAPER. This DAW is powerful and only costs about 60 USD.
I hope this helps you for the DAW question. Composition tips is another reply.
John-Henri