sadly, 15W is not a lot of power, when used alone. i don't remember what the loaded voltage of those panels are. perhaps 13v, which means they support a load of around 1.15A. bear in mind, that is with very clean panels, and in direct burning sunlight.
I had a similar panel and charger kit, and it averaged about 0.7A in direct sunlight.
for a battery, i would suggest something in a small sealed maintenance-free battery. one similar to this: Tenergy 12V 7AH TB1270 Maintenance free Sealed Lead Acid Battery SLA Battery 844949006392 | eBay
it is small enough that your solar panel would have the capacity to charge it.
not sure how much electrical skill you have, as far as wiring stuff up, but i would then add a 12V socket to plug in a cell phone car charger, for charging your phone.
as far as lighting a light, i would stick with low power consumption LED lights.
do not use an inverter with this setup. not sure what kind of camping you do, but this setup will take a while to charge. but a 7AH battery, like i linked to (you don't have to get that one, it was a example), will charge a phone several times on one charge. but an inverter will use a lot of battery power, fast.
and as far as using a car battery, it will take your camping trip duration to charge it.
it is still a fair solar panel, and charge controller, don't get me wrong. but there is a common misconception that because the charge controller says 7A, that it will charge at 7A, regardless as to the size solar panel. in reality, it would take several solar panels to get 7A of charging output.
my camper has a single 100W solar panel that i use, so far, to just keep the large deep-cycle marine battery up to charge when i am not using the camper. if i apply much of a load on the battery, the 100W panel will not keep up, because the battery size and load are too much for my current setup to handle.
but like i said above, your setup will be fine to charge a small battery, and use that small battery to charge a cell phone through a car charger.
Hope this is helpful for you!
and welcome to the forum! 
I had a similar panel and charger kit, and it averaged about 0.7A in direct sunlight.
for a battery, i would suggest something in a small sealed maintenance-free battery. one similar to this: Tenergy 12V 7AH TB1270 Maintenance free Sealed Lead Acid Battery SLA Battery 844949006392 | eBay
it is small enough that your solar panel would have the capacity to charge it.
not sure how much electrical skill you have, as far as wiring stuff up, but i would then add a 12V socket to plug in a cell phone car charger, for charging your phone.
as far as lighting a light, i would stick with low power consumption LED lights.
do not use an inverter with this setup. not sure what kind of camping you do, but this setup will take a while to charge. but a 7AH battery, like i linked to (you don't have to get that one, it was a example), will charge a phone several times on one charge. but an inverter will use a lot of battery power, fast.
and as far as using a car battery, it will take your camping trip duration to charge it.
it is still a fair solar panel, and charge controller, don't get me wrong. but there is a common misconception that because the charge controller says 7A, that it will charge at 7A, regardless as to the size solar panel. in reality, it would take several solar panels to get 7A of charging output.
my camper has a single 100W solar panel that i use, so far, to just keep the large deep-cycle marine battery up to charge when i am not using the camper. if i apply much of a load on the battery, the 100W panel will not keep up, because the battery size and load are too much for my current setup to handle.
but like i said above, your setup will be fine to charge a small battery, and use that small battery to charge a cell phone through a car charger.
Hope this is helpful for you!