Considering your mom has a 510, I can't help but recommend a 306 (which is auto battery). Both are made by Joye, and both have interchangeable parts; the
batteries and atomizers work with each other (just not the cartridges). And if worse comes to worse, you can switch to a 510 and still have parts you can use. Also, cigtechs.com has starter kits on sale (48.50 down from 58.99); they're just still working out payment system problems which should be resolved Monday afternoon/Tuesday morning.
Barring that, from what I've read it's DSE901 or M401.