Let's assume 7w and it runs 24hrs per day (as someone mentioned, far better to actually measure), that works out to 168w or about 14 amp-hr at 12v. Figure 20amp-hr to account for inefficiency. That results in needing a 40amp-hr battery as you can't take a lead acid battery below 50% without damage. Wouldn't be a bad idea to bump it up to 80amp-hr, so if you have a couple overcast days it doesn't kill the battery.
That's likely going to exceed what a lawn tractor battery can do. It might work for a week or so as the battery fully discharges but eventually it will kill the battery.
You might need to bump it up a touch for the charge controller. They don't take much but you are working with a really small system so it might be an impact.
If you go with a 12v camera, you can wire it directly to the battery without a converter which is simpler and more efficient.
As far as the solar panels, you need to put out about 200watt-hr per day. Figure you get about 4hr total of the rated output (it varies across the day and you almost never get the full rated output), so figure at least a 50w panel. Bumping up to 75w would be a good idea to help recover after an overcast day.