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Hmm, so it's a question of what gets the most watt-hours stored for the least money?
Is there a size limit to the total battery pack?
Is the solar controller part of the budget or already paid for?
I hope I'm not being overly pedantic, we may have already narrowed it down to where someone can jump in with a recommendation.
From what I've seen, the controller is the expensive part. If you have that, then it's a search for the cheapest battery type that is compatible with the controller. If it is made to take care of lead acid, then those are probably your best route for less expensive storage.
Downsides are that they do need maintenance and some knowledge of how they work to keep lead acid going for the long haul with top performance, and they take up more space than lithium based batteries.
You're right! A lead acid battery should not be discharged past half of its capacity, it shortened the lifespan of the battery if you do.
So, you need at least double your regular watt-hours that you use overnight in storage plus the batteries will need ongoing maintenance for it to last as long as possible.