A cheap modified-sine-wave inverter will drive that laptop without any problem. I run my stove burner igniters, a 65w soldering iron, a pihole, a gigabit network switch, a router, a NAS drive and two ethernet tv tuners plus an ota dvr off a 420w cheapo unit from Walmart. I also have a Potek 500w msw inverter from amazon that’s fine for about $50. The 420w draws 135ma idle current and the 500w draws ~300ma so neither one wastes much power. Pure sine wave wastes much more power but is important for inductive loads like motors not necessary for electronics.
Given your modest needs a couple of 100w panels and a cheap mppt controller would suffice. For that little bit of power you can connect the solar panels to the controller using low-voltage landscape wire from lowes or home depot. It says on the package it’s only good for 35v iirc but the manufacturers web site says it’s good up to 104v. It’s direct-bury so you don’t need conduit and it’s cheap.
Also because of the low power you can use 10ga wire to connect the controller to the batteries and maybe 8ga from the batteries to the inverter.
Keep the battery wires as short as possible, use a battery disconnect switch and some kind of fuse and I’d consider getting a cheap coulomb counter to tell you the actual state of charge of the battery.
I’d also put switches at least and breakers if possible on the solar panel inputs to the controller.