Using raw math...
50W will push 4 A into a 12V battery. (Theoretically. Your real figure will almost certainly be less.)
A safe charge rate is commonly said to be C/10. On that basis this means your battery can be 30 or 40 Amp-Hours.
Now suppose a day of charging lasts 10 hours. Then 40 Amp-Hours will go to the battery in one day. So on that basis, a suitable A-Hr rating for your battery would again be 40 A-Hrs.
If your battery is a gel cell, then you should be particularly cautious to avoid too fast a charge rate.
Yes, you can do without a commercially-manufactured charge controller. But you must take some steps to prevent the battery from getting overcharged. Example, monitor its volt level continually, and stop charging when it gets above 14.5 or 15V.
Probably the insulation rating between the frame and the electrically-live parts (PV cells and wiring).