Here's a pump chart to help guide you. Look at the specs for a 1/2 hp pump at 120V. Starting amps is 42.5A. That works out to be 5100W for the first 500 milliseconds or so.
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Very doable on just a 24V system. Forget about 12V completely. You'll need a high surge-capacity low-frequency inverter for this. I have Schneider's Conext 4024, and it can surge to 7000W for 5 seconds. That will handle your pump. 48V is even better, but I don't really think you need that much power. I do however run my 1hp 240V well pump on my XW+6848 inverter. That can surge to 12,000W for 60 seconds.
I like to recommend the 2X rule to everyone. Assuming your pumps runs on 960W as you mention above, I've have double those watts, or 2000W of panels. That's what I have for my own 24V system, which has been working very well. I don't run my well-pump on it, but it does easily handle a 1.6hp air-compressor.
If you do go the 48V route, I'd have at least 3000W of panels for it. Don't buy panels retail. Shop on Craigslist, and shop for panels locally, with cash and carry pickup. I'd expect you to get panels in 1000W increments for between 260-400$.