You can't use cards larger than 32 GB with the standard SD.h library.
SdFat supports larger cards if they are formatted FAT32. The default format for SDXC cards is exFAT.
The SD shield/module will not matter for performance as long as voltage levels are correct. Coin cells don't provide sufficient current.
Performance of microSD cards is not easy to predict on Arduino. Arduino uses SPI to access the cards and the SD library has a single 512 byte cache.
Modern SD cards are designed to be used on the high speed 4-bit SDIO bus with very large multi-block writes and reads.
Modern SD cards have very large, 16 KB or larger, flash blocks and emulate the single block access that Arduino libraries use. This can mean much internal data movement, erasing of flash, and rewriting of data.
If you use the standatd SD.h library you will be limited to 4 MHz half speed SPI so performance will be limited.
If you use print text to the card, overhead in formatting the data may dominate performance.
If you use multi-byte binary writes SanDisk Extreme perform well in most applications.
Here is binary write performance for a 32 GB SanDisk Extreme microSD with SdFat at 8 MHz SPI.
buffer size (bytes): 1, time (sec): 18.15, rate (KB/sec): 28.88
buffer size (bytes): 2, time (sec): 9.63, rate (KB/sec): 54.47
buffer size (bytes): 4, time (sec): 5.37, rate (KB/sec): 97.67
buffer size (bytes): 8, time (sec): 3.25, rate (KB/sec): 161.37
buffer size (bytes): 16, time (sec): 2.17, rate (KB/sec): 241.85
buffer size (bytes): 32, time (sec): 1.77, rate (KB/sec): 296.77
buffer size (bytes): 64, time (sec): 1.74, rate (KB/sec): 300.60
buffer size (bytes): 128, time (sec): 1.77, rate (KB/sec): 296.88
Here is performance for a 16 GB SanDisk Ultra microSD.
buffer size (bytes): 1, time (sec): 18.28, rate (KB/sec): 28.68
buffer size (bytes): 2, time (sec): 9.76, rate (KB/sec): 53.73
buffer size (bytes): 4, time (sec): 5.88, rate (KB/sec): 89.11
buffer size (bytes): 8, time (sec): 3.92, rate (KB/sec): 133.82
buffer size (bytes): 16, time (sec): 2.87, rate (KB/sec): 182.67
buffer size (bytes): 32, time (sec): 2.63, rate (KB/sec): 199.08
buffer size (bytes): 64, time (sec): 2.60, rate (KB/sec): 201.88
buffer size (bytes): 128, time (sec): 2.60, rate (KB/sec): 201.62
So, the SD card is only important for larger binary writes. There will be little difference for reads.