I love Harbor Freight, but their solar
offerings are quite limited. They are cheap and inexpensive too. You are about to enter an exciting new world.
Bless you that you and your family have gotten by on 100W, but more importantly on a small Harbor Freight battery with its limited storage.
Note that I have fully (but in good fun) "vented", we can get too the heart of the matter.
If you are off grid, good batteries are your best friend. I don't know if you have a Sam's Club nearby, but if not Batteries Plus is a good option. If you buy online
and pick up in the store they give you 10% off. Sam's has the Duracell GC2 which is a good solid $90 +/- 175AH 6V deep cycle golf cart
battery. You will need 2 of them wired in series to get 12V. I was going to recommend the EGC2, but apparently they are no longer manufactured. Batteries plus has a replacement for it called the Duracell Ultra GC2. It is a 220 AH and for the extra money would be my choice. I have a 48V bank with 8 GC2s and 16 EGC2s. If I had it to do over again they would all have been EGCs for the small increase in $s.
I would suggest that you up your voltage to 24V at some time. Not knowing what your budget is for this upgrade, I will not suggest what to do, but if your budget supports it, I would buy 4 batteries and wire them as a 440 AH @12 V battery which could be rewired to 220AH @24V later on.
The reason for going to a higher voltage is improving your efficiency as you grow your system. That is why I am at 48V. As for panels, I really like the folks at wholesalesolar.com . They have all the parts you will require and at good prices.
As for charge controllers, you want to buy an MPPT charge controller as they are waaaay more efficient. Here is a link that explains the different types of controllers: https://www.altestore.com/store/info/solar-charge-controller/
This is a start. Tell me what your budget is and what you would like to run of your new system and your zip code so I.can see what the solar potential is for the area. If you live in Phoenix you have a lot more sun to play with than in ever-cloudy Seattle. Also give me an idea of budget and I can make sooner better suggestions.
I have had an off grid system myself for 3 years now and am a degreed EE and a PE, so I do have a decent understanding. I would be happy to help as I know some others on the site will also.