I would use a wooden structure with lead acid. If given a choice, instead of lead acid find some cheap LFP.
If the lead acid are free, sell them and apply the profit towards LFP. The only time I would use lead acid would be if I needed to charge in below 32°F (0°C) temps.
Long term, LFP is cheaper per watt than any lead acid. Any metal structure around lead acid will corrode from any fumes vented by the lead acid. Useable capacity of lead acid is 50% of rating, while LFP can be used to 90% of capacity. If lead acid is commonly used over 50% capacity, sulfation will set in quickly and kill the battery quickly. LFP requires an absorption charge regularly, daily basically, and this takes time. Time is limited using solar for charging.
There is a place for lead acid, don't get me wrong. Examples would be extremely cold climate in winter and no way to keep batteries warm. Lead acid will suffer reduced capacity in cold as will any battery, so keep that in mind. A cabin used just on weekends where heat is not supplied during the week and batteries could be recharged to 100% SOC with absorption is a good application. There are others, but that gives you an idea of when to use lead acid and when not to use it.
Is this tied to any current grid AC system?
Any exposed ground wire under NEC is required to be minimum 6AWG.
No.
More details on what plans you have for your system would probably be a good idea. Members here can help you but without more details it may not be good advice. The revelation of possible lead acid batteries changes things considerably.