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#11
I don't know whether 2Gb would offer any practical advantage.
However, at Newegg, the least expensive 1GB GT710 is about $35US. The least expensive 2GB card is about $43.
EVGA GeForce GT 710 DirectX 12 01G-P3-2710-KR 1GB 64-Bit DDR3 PCI Express 2.0 Video Card - Newegg.com
GIGABYTE GeForce GT 710 DirectX 12 GV-N710D3-2GL REV2.0 2GB 64-Bit DDR3 PCI Express 2.0 Low Profile Video Card - Newegg.com
(The cards are from eVGA and Gigabyte, respectively. Both are tier 1 manufacturers.)
I think that a waste of $8 might be acceptable.