Regarding the mast at a beginner level, the only thing you should worry about is the length. The typical ones range from 60 to 90 cm long. There are smaller ones for kitesurfing, and there are larger ones for cruising waves. Even giant ones, for fun.
The smaller the mast, the easier it is to keep your balance, although don’t think there’s a big difference. The advantage of a larger one is that you have more room for pumping without the board touching the water, and this is very good at the beginning.
For the first jumps, a 60 cm mast may be good to make your balance a little easier, but as soon as you start pumping seriously, it will be too short and a 70/80 cm mast will be better for you, so unless you already have a 60 cm mast, I don’t think it’s worth buying one that small. When you already control the pumping and need less range, the normal thing is to go for 70/75 cm.
Personally, I did the first sessions with a 90cm one, but soon I got an 80cm one. At my low level I didn’t notice a difference, although I suppose it would make some difference. I used the 80cm one until I learned to pump, and from session 21 I started to experiment with other masts between 65 and 75.
With a 65cm one can pump, but you have very little margin for error. 70cm is fine in flat waters, but if you’re going to wakethieving or catch some waves it’s too short again.
Conclusion: you can learn with any size mast, but to do it faster I would use one between 75cm and 80cm. Once you’ve learned, you can optimize according to your taste.

As for the material, aluminium or carbon. It depends a lot on the manufacturer. If the front wing has a span less than 115, an aluminium one will normally be enough for you to learn. If it has a larger span, for example in Gong, you will need a carbon mast to avoid breaking it, but other brands have aluminium masts that support large spans.
In short, to start with an aluminium one is enough unless the manufacturer recommends carbon due to the size of the wing so as not to break it.