First of all, it depends on how much current would you draw...
If you plan to build projects with large motors, you won't be able to charge the batteries at all.
I recommend you find all electronics on ebay, and you will need batteries and solar panels + some kind of "charger" (voltage regulator).
For batteries i would personally go for some kind of Li- batteries, but my favorites would be LiFePO4.
For solar panels i would pick whatever size you need (depends on space available, power needed, etc.).
First you need to calculate the whole thing, to see how big system would you need...
If you can't make such calculations, feel free to post detailed specifications about your system.