You need a 10 amp/hour battery to run a 500Ma pump for +/- 14 hours or 20 ah to run it double the time.
So if you assume you have 5 hours of full blast sun a day, you want the battery to be charged in this time. That would leave you with at least a 20 ah battery to cover the other 19 hours. With 6 volts this is 120 watt to cover in 5 hours to charge, that would be about 30 watt cells. In very ideal conditions you still would need to add about 20% extra.. All very roughly calculated, because the battery has about 20% efficiency reservation and the charger has an efficiency loss too. And if the conditions are not ideal which they averagely are in western europe a 50 watt cell still wont keep up.
Next to that batteries have a charge cycle life time, so if constantly in use and daily recharged they can wear out significantly fast. Maybe 500 cycles are about average and the very expensive maybe double.
Take for example your notebook battery and leaf it in the notebook all the time, constantly draining and charging. Less than a year and you lost already about 75% capacity.