The best cheapest battery to safely suit your needs is the one I linked to in #7 above, the Samsung 25R cell is a top cell and 20a rated it will have 4 cells in parallel and are 80a capable. However the BMS current rating limits the current draw to a possible 39a continuous, ideal for your voilamart controller as it has a max 26a current draw.
The cells have plenty of headroom to remain cool and unstressed.
The battery is rated at 9.8ah or 470wh , one will get the ten miles required.
In reality though the actual ah rating for the 26a current draw will be nearer a max 3.5ah or 168wh for that battery with your controller.
This graph explains why the Wh usage will be lower.
Select the 25a discharge curve and follow it down until it transacts the 3.2v discharge line ( 3.2v will be the likely level of a lot of controller LVC level, though some may go down a bit lower to 3.0 or 3.1v per cell).
The 25a bisects the 3.2v line at approx. 875mah which is about the max capacity one can expect form the 25R cell at a continuous 25a current draw as there are four cells in each parallel group this gives a usable capacity of 3.5ah/3500mah using the 25a current discharge usage.