my experience with First Gear is limited so no help, but I would suggest when you look at a heated liner you go with one that has sleeves wired for heated gloves. It was suggested to me that I buy a heated vest because that would keep my core warm thus keeping blood circulation into my arms at a high enough level to warm me all over. My heated vest keeps my core warm but my arms don't seem to benefit. Plus when I wear heated gloves I have to run wires inside my jacket that are a PITA when it's time to fill up, and makes sealing the gap between glove and jacket a massive PITA!!
My gear is Tourmaster, reliable and reasonable but when I replace it, it will be with full sleeves and a remote thermo control whether handlebar mounted or through an app. Sometimes the more expensive choice is cheaper in the long run. Good Luck!