1kWh is about 85 Amp Hours. You'll need at least a 160Ah battery if you don't want any extra storage. Usually you will need to at least double that for days when you don't have much sun. I would suggest you need at least 400Ah worth of batteries.

Then you have to figure out how much sun your panels are getting to determine if you can fully charge your batteries in that time for the rest of the day.

You'll most likely only need a few 100W panels. This means you'll be looking at <$1k for the batteries and <$1k for everything else, including a cheap controller.

Size? Well expect this entire thing to weigh around 500lbs!