Don't be fooled by the chipsets on the motherboard.
Some motherboard manufacturers licensed their designs to other companies and it's possible that you could sometimes see another chipset on the same motherboard.
A good example would be the ones you found on some sound cards of exactly the same model number and design. Some revisions had the Analog Devices AD1848 codec chip, while others had the Cirrus Logic CS4248 codec chip. Manufactured by two different companies, but they performed exactly the same function.
So long as the layout of your motherboard matches the layout of the links in the above posts, then at least you know what the function of each jumper is and what the overall specifications of your motherboard design is.
For a 386DX-40, 8 MB should be sufficient since, back in the day, that was plenty of memory for a Windows 3.1 PC (most people only had 4 MB RAM on board). Also, I doubt that you will find a lot of software that will benefit from having more than 8 MB RAM, since your CPU would start to become the bottleneck long before memory becomes an issue (I'm not saying there isn't, just that there aren't probably many software titles that that will run satisfactory on this CPU and will benefit from having more than 8 MB of RAM).
However, since your motherboard appears to support up to 32 MB of RAM, I don't see any harm in increasing the amount of RAM, since it could improve Windows 3.1 performance (less swap file usage - although, I haven't checked how much Windows 3.1 uses, etc.).
Since this is a 32-bit system, and each 30 pin simm has an 8-bit data width, you need to fill up a bank with 4 simms to make up 32-bit.
If you really want to increase the memory, then you can leave bank 0 filled with the 4x 1 MB simms and then just fill up bank 1 with 4x 4MB simms.
This will then give you 20 MB of RAM in total. However, I would be inclined to say that you shouldn't install more than 16 MB of RAM, since there are some games that had problems if you installed too much memory.
Just check what the current memory speed of your simms are and either get the same speed or faster, but not slower (most were either 60ns or 70ns). Also, I don't recall there being 2 MB simms.
However, before you spend money on 30 pin simms, maybe just try out the PC with the 8 MB RAM first and see how it goes.