There are typically 3 weights of gloves. Very light deerskin or similar for the dexterity needed for Tig. A couple of heavier weights with more insulation for Mig, and then the heaviest for Stick.Usually in the welding stores they have mig and tig welding gloves. I wouldn't buy them online, I would go to a good welding store and try some on. The mig gloves will be thicker. It all depends on how comfortable you feel with a grinder and how much safety you want. I typically just use some non-flammable mechanic's gloves for grinding.
If you start welding and don't feel comfortable enough to start throwing sparks on your rig, I can come down and help out. You're not that far from me.
I have a heavy Tig set and a light Mig set that I use a lot and then when I start burning in a project, I grab the heavier stick gloves (also usually a lot cheaper) to do that because the heat ruins them quickly. I don't want to ruin the lighter more expensive versions so fast. I have no use for any of the popular mechanics gloves. They don't have the protection that leather affords.
Once you figure out the size you wear as you suggested, then you can usually find them online cheaper.