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I hope this is the right place to ask this and that it is "retro" enough. I have a Socket 7 machine that I am working on. It's my 1st PC from childhood that I restored, and now I would like to upgrade it.

The system is a FIC VT-502 with a Cyrix 6x86MX PR166 and (currently) 48MB of SIMM memory. The motherboard supports both EDO SIMM and SDRAM DIMM, as seen here: https://www.vogonswiki.com/index.php/Socket_7_Builds#Choosing_RAM

I want to upgrade to using 128MB of RAM and, if possible, use SDRAM (because I can, and because it seems to be cheaper). I found some SDRAM on a site called MemoryX (or MemoryTen), but when I installed it, each stick was only read as 16MB, for a total of 32MB! Here's what I bought, claiming to be 64MB each stick: https://photos.app.goo.gl/SurvJWmKxdrPbZ5Q8

Doing some research, I found http://redhill.net.au/b/b-98.html#ram which explains this issue:

most older mainboards do not understand 64Mbit [megabit] chips and see a standard 64MB [megabyte] DIMM as eight 16Mbit [megabit] chips

So, my question is what should I be looking for when trying to buy 128MB (2x64MB) of SDRAM for my system? Do I want single-sided or double-sided RAM? How many chips should be on the stick? Or should I just stick with SIMM and get 128MB (4x32MB) of SIMM?

The change from DRAM to SDRAM changed how addresses are communicated from the processor to the RAM. In DRAM, addresses are divided up as a row and column address, each using roughly half the bits supported by the chip. The row is sent whenever it changes and the column for every access; its an arrangement designed to reduce the number of address pins required for any given address space.

In SDRAM an extra part is added, the bank address. This address usually has only a few bits, and in small DIMMs is entirely unused. However, starting at 32MiB there are no longer enough address lines on a DIMM to work with just row and column addresses, so the system must use bank addresses. As the specification supports up to 4 banks, this means 64MiB is the largest 168 pin DIMM available.

What this means is that early machines that supported DIMMs but weren't designed with this kind of memory size in mind only implemented the logic to work with a single bank, so could only use up to 16MiB per DIMM. This was likely especially common on boards that also supported SIMMs, simply because then the way of working with the two types of memory is more similar.