The first Amazon item is an under powered non-durable overpriced type solution.
Suggest skipping buying stuff until you spend a burn researching at the AEZ - alternative energy zone and other camps. Their theory is that you will destroy your first solar-battery-charger system. If your town has a DYI solar group, that's a great approach too. And the AEZ has a message board for questions.
If you want to do something this year I would go with a deep cycle boat battery, a little red wagon for transporting it for charging it at Snow Koan Solar, and the most efficient inverter you can find (you can use the inverter in your vehicle year round), unless you have DC lights. A deep cycle battery is easily disposed of on CL if you decide you don't need it in the future. Wet cell will be cheaper, more advanced AGM may end up as part of your long term solar strategy, even for emergencies at home.
LED light strings can be .1 Watts per bulb and .1 Amp @ 110 Volts draw running total for a 100 light string, so investing in LED lights is a no-brainer and they are usable year round. You can test your run time against the lights at home and buy a second battery if needed, but 5 strings drawing .1 A each 10 hours is 5AH and a full size boat battery is 75-200AH. A marine battery box is a good idea. We have run a sound system at BM for a 4000 SF area off that size battery for 6 hours, no subs, digital amps, moderate volume, but as mentioned heating loads, like cookers, coolers, refrigerators and hairdryers will drain you dry.
increasing the signal to noise ratio with compassion