I believe this would be more suitable for electrical section.
However, here is my take: for invertors I'd recommend having a secondary battery with higher discharge rate (higher charge rate respectively), especially when you are looking at high power appliances (at least 2000W). In this case, depending on other items / consumers you are looking to have at least 100Ah battery. In this case, I'd recommend having a quality 12V DC-DC charger such as RedArc BCDC1225/BCDC1240/BCDC1250 (note that there is a version with solar input for these). If you are in Australia, then you can check other brands such as EnerDrive (I am probably biased as there is only CTEK and RedArc in EU and I am a dealer for the Balkans for RedArc which I am happy with).
There is a possibility for a setup to link two batteries (starter and aux) together. This could be done via a voltage sensing relay such as RedArc's SBI: here is a diagram for that
https://www.redarc.com.au/bcdc-dual-wit ... tery-setup (in addition, here is a video of such setup:
https://www.youtube.com/watch?v=SgBc249DbwQ).