Most of the printers I've seen use either 3mm or 1.75mm thick filament. From your description, it's hard to guess. See if you can find some calipers to measure the width of the filament with. Just in case you need to work with Imperial units, here's a guide: 3mm is pretty close to 1/8". 1.75mm is pretty close to 1/16". I expect that either of these will be readily available on Amazon, and places that specialize in 3D printer supplies. You also should look at your documentation and see what material you should get. Two of the common materials are ABS and PLA. Some printers will use either (with different settings), some will only use one or the other. For example, my Dremel printer only uses 1.75mm PLA (and they only support it if you buy Dremel-branded filament). My old Makerbot Thing-o-matic used 3mm filament but it would work with both ABS and PLA.
Hope that helps.